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{"sheet":"Users Manual","index":0,"n_rows":131,"n_cols":1,"rows_kept":131}
["Gaussian Based Air Pollution Modeling User's Manual"]
["Written by: Karah Conklin"]
["Advisor: Prof. Haith"]
["Fall 2010"]
["Cornell University, Department of Biological and Environmental Engineering"]
[]
[]
["Table of Contents:"]
["Background"]
["Introduction"]
["     Coordinates"]
["     How the Model Works"]
["Instructions"]
["     User Input"]
["     Default Values"]
["     Running the Model"]
["Pollutant Controls and Cost Estimates"]
["Air Quality Standards"]
["Examples"]
["References"]
[]
["Background:"]
["There are several classes of common pollutants that are regulated including total suspended particulates (TSP), sulfur dioxide (SO2), and carbon monoxide (CO).  All of these pollutants have varying sources and characteristics that affect the methods used to control emissions and the cost of that control.  Below is a list of common pollutants, their main sources, and their effects:"]
["TSP - Total Suspended Particulates"]
["Total suspended particulates are solid and liquid particles including dust, pollen and ash.  These pollutants are classified by size as either aerosols, smaller than 50 microns, fine particulates, smaller than 3 microns, or settable particles. The main sources of this pollutant is from natural events like forest fires, wind, and construction. This pollutant usually causes aggravation of asthma and other respiratory symptoms but can cause impaired visibility, cloud formation and impairment of plant photosynthesis."]
["SO2 - Sulfur Dioxide"]
["Sulfur Dioxide is a colorless gas that is usually released from the combustion of fossil fuels and oxidizes to form sulphuric acid in water.  Other sources of sulfur dioxide include smelting of sulfur containing metals and industrial processes.  This pollutant causes respiratory diseases like asthma, bronchitis and emphysema.  It can also cause the corrosion of metals and the deterioration of many surfaces."]
["CO - Carbon Monoxide"]
["Carbon monoxide is a colorless gas that attaches to hemoglobin in the blood.  The main sources are the incomplete combustion of fossil fuels from motor vehicle exhaust or forest fires."]
["O3 - Ozone"]
["Ozone is a colorless gas that can contribute to photochemical smog.  It is mainly formed through reactions of other chemicals with sunlight in the atmosphere.  This pollutant causes respiratory diseases in humans, deteriorates rubber and paint and causes reduced growth and premature fruit and leaf drop in plants. "]
["NOX - Nitrogen Oxides"]
["Nitrogen oxides are a group of pollutants that are caused by motor vehicle exhausts, high-temperature combustion, and atmospheric conditions.  Over exposure can result in respiratory illnesses, fading of dyes and paints and reduced growth in plants."]
["VOC - Volatile Organic Compounds (and Hydrocarbons (HC))"]
["These are a group of compounds that result from the incomplete combustion of fuels in motor vehicles and processing, petroleum products and natural events.  They are suspected to be linked to cancer and are often a precursor to other atmospheric pollutants.  "]
[]
["Introduction:"]
["This model is based on the Gaussian plume model which is typically applied to point source emitters such as coal-burning power plants and other industrial processes.  This model assumes that steady state conditions exist on a short time scale. The pollution from the source is assumed to be an idealized plume coming from a stack with a specific height."]
["Once the plume is released from the source, dispersion begins in three dimensions.  Dispersion downwind of the source will be dominated by advection (wind speed). Lateral dispersion will depend on atmospheric conditions and air stability.  From this, the Gaussian model assumes that the dispersion will take the form of a normal (Gaussian) distribution with a maximum concentration at the center. "]
["This model also assumes that there are no chemical changes or losses within the system and that concentration is directly proportional to the mass emitted. "]
[]
[]
["The standard equation uses is as follows:"]
[]
["C(x,y,z)  = the concentration emissions (in ug/m^3) at any point x meters downwind of the source, y meters laterally from the centerline of the plume, and z meters above ground level. "]
["Q = or mass of the emission per unit of time (g/s) "]
["u = the wind speed (in the x-direction) (m/s)"]
["H = the height of the source above ground level (m) "]
["              = the standard deviations of A Gaussian plume in the lateral and vertical directions"]
[]
[]
["Coordinates:"]
["This Gaussian transport model is based on an x-y-z coordinate system that the user must set up before running the model.  This coordinate system is set up such that the x-axis is parallel to the prevailing wind direction and that the sources and receptors always have positive coordinates. "]
[]
[]
["How this model works:"]
["In this worksheet model, a user can identify the current pollutant concentrations at a set of specified receptors based on input source data (simulation approach).  There is also an option where with added cost data, a cost-effective solution can be found that meets specified maximum concentrations (optimization approach).  "]
["In order to run this model, the user must input the coordinates, emissions, and stack height for up to 25 sources and the coordinates and maximum allowed concentration levels (i.e., ambient air quality standard) for up to 25 receptors. The model also requires a mean wind speed (in the x-direction) and the user must choose a solar insolation indicator.  "]
["Based on these inputs, the worksheet calculates the transport factors (t(x,y)) for each source/receptor pair.  For the simulation model approach these values are them multiplied by the emissions (Q) it give a concentration at a receptor from a single source.  The sum of all of the sources then gives the total concentration.  For the optimization approach, the model changes the emissions from each source in order to meet the receptor concentration standards while minimizing the cost.  "]
[]
[]
["Instructions:"]
["In order to run this program, you must have the Solver add-in loaded in excel.  If you do not already have this you can load it using the instructions below."]
[]
["For Excel 2007and newer: "]
["1. Click the Microsoft Office Button           ,and then click Excel Options."]
["2. Click Add-Ins, and then in the Manage box, select Excel Add-ins."]
["3. Click Go."]
["4. In the Add-Ins available box, select the Solver Add-in check box, and then click OK."]
["       Tip    If Solver Add-in is not listed in the Add-Ins available box, click Browse to locate the add-in."]
["5. If you get prompted that the Solver Add-in is not currently installed on your computer, click Yes to install it."]
["6. After you load the Solver Add-in, the Solver command is available in the Analysis group on the Data tab."]
["For older versions of excel, please refer to the help icon located in the upper right-hand corner"]
[]
["Macros must also be enabled in order for the model to run.  A security message will appear near the top of the page if macros are disabled.  Click on the options button and select enable for macros and links."]
[]
["User Input:"]
["This model is made to work on an x-y grid system that must be set-up by the user in advance of running the model.  Necessary parameters for the model are: Wind Speed, Insolation, Maximum Acceptable Concentration, Receptor & source Coordinates (based on grid), Source Emissions, Stack Height and Cost of Removal at Source.  "]
["On the next tab, user input, you will input the parameters for your scenario.  All of the variables are required!  SECTION 1: The first parameter you will need to input is wind speed.  The input wind speed is for wind in the downwind direction.  This should be parallel to the x-axis of your coordinate system.  Wind speed is measured in m/s.  Solar insolation is the next parameter input and requires you to choose an insolation value from the list of check boxes.  Only check 1 box.  The insolation value along with the wind speed allows the model to choose an atmospheric stability classification (automatic) varying from very unstable to stable.    The last input in this section in the number of sources and receptors.  SECTION 2:  In this section, you will input the parameters for your sources and receptors.  Starting on the left, is the input section for the sources.  The X and Y coordinates (km), Pollutant Emissions(kg/day), Stack Height, Emissions(m), and Cost of Removal ($/kg removed) are required.   To the right of the source inputs are the receptor inputs.   The required inputs are the X and Y coordinates (km) and the maximum acceptable concentration (ug/m3).    You can input up to 25 sources and receptors into the model.  If you are running the model with less than 25 sources or receptors, leave the values for those sources/receptors at their default values (see below).  These will not affect the output of the model. "]
[]
["Default Values:"]
["X & Y Coordinates (for both sources and receptors), Source Emissions, Source Stack Height   =   -99"]
["Wind speed, Number of Sources and Receptors, Cost of Removal, Maximum Acceptable Concentration   =   0"]
[]
["Running the model:"]
["The model can be run in two different modes: optimization or simulation.  It is recommended that you run the simulation model first to identify if there are any areas that are currently exceeding the concentration standards.  After choosing the \"run simulation button\", you will be directed to a page where the current air quality is displayed.  Any receptors where the minimum concentration levels are not met will be highlighted in red. "]
["The optimization model can be run to produce the most cost effective emissions control solution.  From the bottom of the user input tab, choose the \"run optimization\" button.  A \"Solver Results\" box will appear.  Make sure that \"Keep Solver Solutions\" is selected and press OK. This will take you to the optimization output page that shows you the most cost effective emission controls for your scenario. Graphs are also proved to aid in the understanding of how the emissions are controlled."]
[]
[]
["Pollutant Controls and Cost Estimates:"]
["There are many ways of controlling air pollutants at the source.  Many of the process can be used to reduce multiple pollutants and are  described below. All costs are estimates. More information on estimating cost can be found in the EPA's Air Pollution Control Cost Manual and CATC product web pages."]
["Controls:"]
["TSP - Total Suspended Particulates"]
["     Controls - cyclones, momentum separators, filters, scrubbers, electrostatic precipitators"]
["     Cost - $0.00047 - $0.71 per kg removed"]
["SO2 - Sulfur Dioxide"]
["     Controls - scrubber, catalytic conversion"]
["     Cost - $0.11 - $0.55 per kg removed"]
["NOX - Nitrogen Oxides"]
["     Controls - scrubber, catalytic conversion"]
["     Cost - $0.11 - $0.55 per kg removed"]
["VOC - Volatile Organic Compounds"]
["     Controls - Carbon Adsorption, Recapture, scrubbers, Flare/thermal oxidation"]
["     Cost - $0.017 - $0.55 per kg removed"]
["       *** Cost data was complied from the EPA's \"General Information of CATC Products\""]
[]
["Air Quality Standards"]
["National Air Quality Standards (Standards may also vary by state)"]
["Carbon Monoxide - 10 mg/m3 over 8 hours"]
["Lead - 0.15 ug/m3 over a 3 month average"]
["NOX -  53 ug/m3 annual average"]
["Particulate Matter 10 - 150 ug/m3 over 24 hours"]
["Particulate Matter 2.5 - 35 ug/m3 over 24 hours"]
["Ozone - 0.12 mg/m3 over 1 hour"]
["Sulfur Dioxide - 75 ug/m3 over 1 hour"]
["Total Suspended Particles - 260 ug/m3 over 24 hours"]
[]
["Examples"]
["Example 1: California Smog Pollution"]
["Example 2: Michigan Industrial Pollution"]
["Example 3: New York NOX Pollution"]
[]
["References:"]
["Turner, D. B. 1994. Workbook of Atmospheric Dispersion Estimates. Lewis Publishers, Ann Arbor, MI."]
["Masters, G.M. 1991. Introduction to Environmental Engineering and Science. Prentice-Hall, Englewood Cliffs, NJ."]
["Vatavuk, W.M. 1990. Estimating Costs of Air Pollution Control. Lewis Publishers, Chelsea, MI."]
["US Environmental Protection Agency. 04 Nov. 2010. \"General Information of CATC Products\". http://www.epa.gov/ttn/catc/products.html  "]
["US Environmental Protection Agency. 2002. EPA Air Pollution Control Cost Manual 6th Edition. .http://www.epa.gov/ttn/catc/dir1/c_allchs.pdf."]
[]
["Example References:"]
["US Environmental Protection Agency. 2009. Emissions Factors & AP 42, Compilation of Air Pollutant Emission Factors. http://www.epa.gov/ttnchie1/ap42/"]

{"sheet":"User Input","index":1,"n_rows":60,"n_cols":11,"rows_kept":60}
["Gaussian Based Air Pollution Modeling"]
["Karah Conklin"]
["Fall Semester 2010"]
["Cornell University, Department of Biological and Environmental Engineering"]
[]
["User Inputs"]
["Instructions: "]
["1) Make sure that Solver is installed and the Macros are enabled on your computer (for help please refer to the users manual)"]
["2) Set up x-y grid system the is parallel to the wind direction. "]
["3) Input wind speed and choose and an Insolation value.  (Choose one, only )"]
["4) Input the Coordinates, Current Emissions and Stack Height for each source.  Leave any rows that are not being used with their original values."]
["5) Input the Coordinates and maximum concentration limits for each receptor.  Leave any row that is not being used with their original values."]
["6) Run the simulation or optimization models by clicking on the buttons at the bottom of the page. "]
[]
[]
["Section 1:"]
[]
["Wind speed",null,"m/s"]
["Insolation","Check only 1 box"]
[]
[]
[]
[]
[]
["Number of Sources",{"$nulls":6},"Number of Receptors"]
[]
[]
["Section 2:"]
[]
["Source Input",{"$nulls":6},"Receptor Input"]
["Number","X Coordinate (km)","Y Coordinate (km)","Emissions (kg/day)","Stack Height (m)","Cost of Removal ($/kg)",null,"Number","X Coordinate (km)","Y Coordinate (km)","Maximum Acceptable Concentration (ug/m3)"]
[1,5,-99,-99,-99,0,null,1,-99,-99,0]
[2,-99,-99,-99,-99,0,null,2,-99,-99,0]
[3,-99,-99,-99,-99,0,null,3,-99,-99,0]
[4,-99,-99,-99,-99,0,null,4,-99,-99,0]
[5,-99,-99,-99,-99,0,null,5,-99,-99,0]
[6,-99,-99,-99,-99,0,null,6,-99,-99,0]
[7,-99,-99,-99,-99,0,null,7,-99,-99,0]
[8,-99,-99,-99,-99,0,null,8,-99,-99,0]
[9,-99,-99,-99,-99,0,null,9,-99,-99,0]
[10,-99,-99,-99,-99,0,null,10,-99,-99,0]
[11,-99,-99,-99,-99,0,null,11,-99,-99,0]
[12,-99,-99,-99,-99,0,null,12,-99,-99,0]
[13,-99,-99,-99,-99,0,null,13,-99,-99,0]
[14,-99,-99,-99,-99,0,null,14,-99,-99,0]
[15,-99,-99,-99,-99,0,null,15,-99,-99,0]
[16,-99,-99,-99,-99,0,null,16,-99,-99,0]
[17,-99,-99,-99,-99,0,null,17,-99,-99,0]
[18,-99,-99,-99,-99,0,null,18,-99,-99,0]
[19,-99,-99,-99,-99,0,null,19,-99,-99,0]
[20,-99,-99,-99,-99,0,null,20,-99,-99,0]
[21,-99,-99,-99,-99,0,null,21,-99,-99,0]
[22,-99,-99,-99,-99,0,null,22,-99,-99,0]
[23,-99,-99,-99,-99,0,null,23,-99,-99,0]
[24,-99,-99,-99,-99,0,null,24,-99,-99,0]
[25,-99,-99,-99,-99,0,null,25,-99,-99,0]
[]
[]
[]
["Running the Model"]

{"sheet":"Output-Simulation","index":2,"n_rows":32,"n_cols":4,"rows_kept":32,"hidden":true}
["Air Pollution Concentration Model"]
["Simulation Outputs"]
[]
[]
[]
[]
["Receptor","Original Concentration (ug/m3)","Maximum Concentration at Receptor (ug/m3)","Concentration Difference (ug/m3)"]
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["Air Pollution Concentration Model"]
["Optimization Outputs"]
[]
[]
["Total Cost of Removal"]
[null,{"$f":"SUM(F10:F34)","v":{"v":0,"d":"$0.00"}},"per day"]
[]
[]
["Source","Original Emissions (kg/day)","Cost of Removal ($/kg)","New Emissions (kg/day)","Emissions Removed (kg/day)","Total Cost of Removal ($)","Percent Reduction",null,"Receptor","Concentration after Emissions Reduction (ug/m3)"]
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{"sheet":"Factors","index":6,"n_rows":61,"n_cols":26,"rows_kept":61,"hidden":true}
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[]
[]
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[null,25,{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}},{"$f":"Constraints!$D28","v":{"v":0,"d":"0.00E+00"}}]

{"sheet":"Constraints","index":18,"n_rows":59,"n_cols":26,"rows_kept":59}
["Optimization Model"]
[]
["Source","Original Emissions (kg/day)","Cost of Removal ($/kg)","New Emissions (kg/day)","Total Cost of Removal"]
[1,{"$f":"IF('User Input'!D32>0, 'User Input'!D32, 0)","v":0},{"$f":"'User Input'!F32","v":{"v":0,"d":"$0.00"}},30000,{"$f":"C4*(B4-D4)","v":{"v":0,"d":"$0.00"}}]
[2,{"$f":"IF('User Input'!D33>0, 'User Input'!D33, 0)","v":0},{"$f":"'User Input'!F33","v":{"v":0,"d":"$0.00"}},8000,{"$f":"C5*(B5-D5)","v":{"v":0,"d":"$0.00"}}]
[3,{"$f":"IF('User Input'!D34>0, 'User Input'!D34, 0)","v":0},{"$f":"'User Input'!F34","v":{"v":0,"d":"$0.00"}},355.7818278571904,{"v":0,"d":"$0.00"}]
[4,{"$f":"IF('User Input'!D35>0, 'User Input'!D35, 0)","v":0},{"$f":"'User Input'!F35","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[5,{"$f":"IF('User Input'!D36>0, 'User Input'!D36, 0)","v":0},{"$f":"'User Input'!F36","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[6,{"$f":"IF('User Input'!D37>0, 'User Input'!D37, 0)","v":0},{"$f":"'User Input'!F37","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[7,{"$f":"IF('User Input'!D38>0, 'User Input'!D38, 0)","v":0},{"$f":"'User Input'!F38","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[8,{"$f":"IF('User Input'!D39>0, 'User Input'!D39, 0)","v":0},{"$f":"'User Input'!F39","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[9,{"$f":"IF('User Input'!D40>0, 'User Input'!D40, 0)","v":0},{"$f":"'User Input'!F40","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[10,{"$f":"IF('User Input'!D41>0, 'User Input'!D41, 0)","v":0},{"$f":"'User Input'!F41","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[11,{"$f":"IF('User Input'!D42>0, 'User Input'!D42, 0)","v":0},{"$f":"'User Input'!F42","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[12,{"$f":"IF('User Input'!D43>0, 'User Input'!D43, 0)","v":0},{"$f":"'User Input'!F43","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[13,{"$f":"IF('User Input'!D44>0, 'User Input'!D44, 0)","v":0},{"$f":"'User Input'!F44","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[14,{"$f":"IF('User Input'!D45>0, 'User Input'!D45, 0)","v":0},{"$f":"'User Input'!F45","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[15,{"$f":"IF('User Input'!D46>0, 'User Input'!D46, 0)","v":0},{"$f":"'User Input'!F46","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[16,{"$f":"IF('User Input'!D47>0, 'User Input'!D47, 0)","v":0},{"$f":"'User Input'!F47","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[17,{"$f":"IF('User Input'!D48>0, 'User Input'!D48, 0)","v":0},{"$f":"'User Input'!F48","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[18,{"$f":"IF('User Input'!D49>0, 'User Input'!D49, 0)","v":0},{"$f":"'User Input'!F49","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[19,{"$f":"IF('User Input'!D50>0, 'User Input'!D50, 0)","v":0},{"$f":"'User Input'!F50","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[20,{"$f":"IF('User Input'!D51>0, 'User Input'!D51, 0)","v":0},{"$f":"'User Input'!F51","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[21,{"$f":"IF('User Input'!D52>0, 'User Input'!D52, 0)","v":0},{"$f":"'User Input'!F52","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[22,{"$f":"IF('User Input'!D53>0, 'User Input'!D53, 0)","v":0},{"$f":"'User Input'!F53","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[23,{"$f":"IF('User Input'!D54>0, 'User Input'!D54, 0)","v":0},{"$f":"'User Input'!F54","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[24,{"$f":"IF('User Input'!D55>0, 'User Input'!D55, 0)","v":0},{"$f":"'User Input'!F55","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[25,{"$f":"IF('User Input'!D56>0, 'User Input'!D56, 0)","v":0},{"$f":"'User Input'!F56","v":{"v":0,"d":"$0.00"}},0,{"v":0,"d":"$0.00"}]
[{"$nulls":3},"SUM",{"$f":"SUM(E4:E28)","v":{"v":0,"d":"$0.00"}}]
[]
["Constraints:"]
[null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]
[1,{"$f":"(XR*((10^9)/86400))*t","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[21,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[22,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["Sum",{"$f":"SUM(B33:B57)","v":0},{"$f":"SUM(C33:C57)","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
["Constraint ",{"$f":"Factors!B57","v":0},{"$f":"Factors!C57","v":0},{"$f":"Factors!D57","v":0},{"$f":"Factors!E57","v":0},{"$f":"Factors!F57","v":0},{"$f":"Factors!G57","v":0},{"$f":"Factors!H57","v":0},{"$f":"Factors!I57","v":0},{"$f":"Factors!J57","v":0},{"$f":"Factors!K57","v":0},{"$f":"Factors!L57","v":0},{"$f":"Factors!M57","v":0},{"$f":"Factors!N57","v":0},{"$f":"Factors!O57","v":0},{"$f":"Factors!P57","v":0},{"$f":"Factors!Q57","v":0},{"$f":"Factors!R57","v":0},{"$f":"Factors!S57","v":0},{"$f":"Factors!T57","v":0},{"$f":"Factors!U57","v":0},{"$f":"Factors!V57","v":0},{"$f":"Factors!W57","v":0},{"$f":"Factors!X57","v":0},{"$f":"Factors!Y57","v":0},{"$f":"Factors!Z57","v":0}]

{"sheet":"Example 1","index":19,"n_rows":75,"n_cols":7,"rows_kept":75,"merged":[[2,0,3,3],[5,0,5,3],[15,0,15,3],[31,0,31,3],[74,0,74,5]]}
["Example 1"]
["California Urban Smog"]
["Smog is a type of air pollution typically found in urban areas that results from vehicle emissions and industrial processes.  There are several different components of smog including sulfur dioxide, nitrogen oxides (NOX), volatile organic carbons (VOCs), and ozone.  In this example we are going to focus on sulfur dioxide emissions from 6 sources in southern California.  Most of the sulfur dioxide in California is produced in electricity generation and industrial processes.  "]
[]
[]
["Southern California has smog pollution problem. The air pollutant of particular concern is sulfur dioxide, which is emitted from six major sources in the area. Three of the sources are electricity generation plants, one is a waste incineration site, and two are chemical processing plants.  Emissions of sulfur dioxide from the six sources are given below."]
[]
["Sources","Emissions (kg/day)","Stack Height (m)","Cost of Removal ($/kg)"]
[1,546,8,0.44]
[2,204,7.2,0.37]
[3,92,11,0.5]
[4,9100,18,0.11]
[5,3720,15,0.13]
[6,11400,19,0.16]
[]
["A preliminary assessment has identified the \"critical\" weather conditions in the area as a 2.7 m/sec wind speed on a cloudy night . Nine ground level receptors have been selected as places where health effects are most important: schools, hospitals, and nursing homes. The national ambient air quality standard for sulfur dioxide is 75 ug/m3.  Near hospitals, receptors 6-9, the state of California has suggested that the sulfur dioxide levels be less than 60 ug/m3.  Locations of sources and receptors in an X-Y coordinate system with (0,0) origin are given below. The X axis is parallel to the wind direction. Determine which sources need to decrease their emissions in order to meet the standard and how much it will cost to do this."]
[]
["Source","(X,Y) (km)","Receptor","(X,Y) (km)"]
[1,"1,9",1,"2,4"]
[2,"12,5",2,"11,5"]
[3,"3,5",3,"14,6"]
[4,"1,1",4,"9,3"]
[5,"9,6",5,"3,8"]
[6,"12,7",6,"7,1"]
[null,null,7,"8,6"]
[null,null,8,"12,9"]
[null,null,9,"11,1"]
[]
[]
[]
["SOLUTION:"]
["After inputting the above information into the model, we ran a simulation to see if the maximum concentration was being exceeded at any receptor.  We found that receptors 3, 6 and 9 had concentrations that were above the acceptable limit (as shown below)."]
[]
[]
[]
["Receptor","Original Concentration (ug/m3)","Maximum Concentration at Receptor (ug/m3)","Concentration Difference (ug/m3)"]
[1,0,0,0]
[2,5.4308573412911425,75,-69.56914265870886]
[3,407.5471256241348,75,332.5471256241348]
[4,2.8263197737042062E-6,75,-74.99999717368023]
[5,4.9491683553966246E-23,75,-75]
[6,769.808710232041,75,694.808710232041]
[7,1.6572244040873702E-4,60,-59.99983427755959]
[8,21.21542767684299,60,-38.78457232315701]
[9,392.66936502852434,60,332.66936502852434]
[]
[]
[]
["We then went back to the input tab where we ran an optimization model.  The results from this were as follows:"]
[]
["Total Cost of Removal"]
[null,{"v":1298.313099138315,"d":"$1,298.31"},"per day"]
[]
[]
["Source","Original Emissions (kg/day)","Cost of Removal ($/kg)","New Emissions (kg/day)","Emissions Removed (kg/day)","Total Cost of Removal ($)","Percent Reduction"]
[1,546,0.44,546,0,0,0]
[2,204,0.37,204,0,0,0]
[3,92,0.5,92,0,0,0]
[4,9100,0.11,886.583888865425,8213.416111134575,903.4757722248032,{"$f":"0.902573199025777*100","v":90.2573199025777}]
[5,3720,0.13,682.789792972986,3037.210207027014,394.83732691351184,{"$f":"0.816454356727692*100","v":81.6454356727692}]
[5,3720,0.13,682.789792972986,3037.210207027014,394.83732691351184,{"$f":"0.816454356727692*100","v":81.6454356727692}]
[6,11400,0.16,11400,0,0,0]
[]
["Receptor","Concentration after Emissions Reduction (ug/m3)"]
[1,0]
[2,5.4308573412911425]
[3,75.00000000145602]
[4,2.7535940020528309E-7]
[5,4.9491683553966246E-23]
[6,75.00000000000001]
[7,1.6572244040873702E-4]
[8,21.21542767684299]
[9,38.25652007530838]
[]
["For this problem, we determined that source 4 needed to reduce their emissions by 90% to 886.6 kg/day and source 5 needed to reduce their emissions by 81% to 682 kg/day in order to meet the sulfur dioxide concentration limits."]

{"sheet":"Example 2","index":20,"n_rows":93,"n_cols":7,"rows_kept":93,"merged":[[3,0,3,5],[32,0,32,5],[62,0,62,5],[92,0,92,3]]}
["Example 2"]
["Michigan Industrial Pollution"]
[]
["Areas of Michigan that are heavy industrial areas often have particulate pollution problems. In our area of concern particulates (total particulates) are emitted from 25 sources in the area. These sources cover a variety of industries including asphalt production, iron & steel production, zinc smelting, and plastic production.  Emissions of particulates for the 25 sources are given below."]
[]
["Sources","Emissions (kg/day)","Stack Height (m)","Cost of Removal ($/kg)"]
[1,{"$f":"155*50","v":7750},15,0.44]
[2,{"$f":"0.25*20","v":5},19,0.006]
[3,{"$f":"16*40","v":640},12.5,0.04]
[4,{"$f":"5.56*130","v":722.8},18,0.3]
[5,{"$f":"5.56*90","v":500.4},15.5,0.0037]
[6,{"$f":"22*32","v":704},19,0.37]
[7,{"$f":"3000","v":3000},20,0.00083]
[8,{"$f":"43*50","v":2150},22,0.0021]
[9,{"$f":"17.5*90","v":1575},19,0.5]
[10,{"$f":"10*30","v":300},15.5,0.301]
[11,{"$f":"22*10","v":220},18,0.0278]
[12,{"$f":"7.25*40","v":290},19.5,0.009]
[13,{"$f":"0.25*50","v":12.5},20,0.00047]
[14,{"$f":"17.5*25","v":437.5},25,0.11]
[15,{"$f":"7*40","v":280},22.5,0.13]
[16,{"$f":"0.25*20","v":5},18.5,0.065]
[17,{"$f":"155*20","v":3100},16,0.00467]
[18,{"$f":"25*25","v":625},15.5,0.0034]
[19,{"$f":"50*45","v":2250},20,0.054]
[20,{"$f":"155*90","v":13950},23,0.16]
[21,{"$f":"18*35","v":630},19.5,0.0092]
[22,{"$f":"5.56*30","v":166.79999999999998},21,0.0039]
[23,{"$f":"5.56*25","v":139},16,0.108]
[24,{"$f":"155*60","v":9300},21,0.0911]
[25,{"$f":"16*20","v":320},20.5,0.0008]
[]
["A preliminary assessment has identified the \"critical\" weather conditions in the area as a 4.2 m/sec wind speed on a low solar day . Twenty five ground level receptors have been selected as places where health effects are most important: schools, hospitals, daycares and nursing homes. The national ambient air quality standard for particulates is 150 ug/m3.   Locations of sources and receptors in an X-Y coordinate system with (0,0) origin are given below. The X axis is parallel to the wind direction. Determine which sources need to decrease their emissions in order to meet the standard and how much it will cost to do this."]
[]
["Source","X (km)","Y (km)",null,"Receptor","X (km)","Y (km)"]
[1,31,17,null,1,36,9]
[2,44,47,null,2,22,25]
[3,34,16,null,3,8,50]
[4,13,37,null,4,30,46]
[5,46,41,null,5,13,31]
[6,2,12,null,6,14,34]
[7,44,41,null,7,40,21]
[8,2,14,null,8,24,6]
[9,13,5,null,9,38,26]
[10,41,17,null,10,49,13]
[11,6,47,null,11,46,1]
[12,44,17,null,12,34,44]
[13,50,41,null,13,21,44]
[14,29,9,null,14,19,35]
[15,27,13,null,15,40,41]
[16,41,8,null,16,45,46]
[17,49,7,null,17,50,28]
[18,20,46,null,18,47,10]
[19,7,34,null,19,19,29]
[20,10,5,null,20,29,47]
[21,3,8,null,21,14,36]
[22,32,1,null,22,27,35]
[23,17,34,null,23,24,38]
[24,26,34,null,24,2,46]
[25,8,0,null,25,48,2]
[]
["SOLUTION:"]
["After inputting the above information into the model, we ran a simulation to see if the maximum concentration was being exceeded at any receptor.  "]
[]
[]
["Receptor","Original Concentration (ug/m3)","Maximum Concentration at Receptor (ug/m3)","Concentration Difference (ug/m3)"]
[1,{"v":2.741815981270499,"d":"2.7418E+00"},{"v":150,"d":"1.5000E+02"},{"v":-147.2581840187295,"d":"-1.4726E+02"}]
[2,{"v":4.951792304225605e-12,"d":"4.9518E-12"},{"v":150,"d":"1.5000E+02"},{"v":-149.99999999999505,"d":"-1.5000E+02"}]
[3,{"v":4.092008118120319e-52,"d":"4.0920E-52"},{"v":150,"d":"1.5000E+02"},{"v":-150,"d":"-1.5000E+02"}]
[4,{"v":1.4371329258890022,"d":"1.4371E+00"},{"v":150,"d":"1.5000E+02"},{"v":-148.562867074111,"d":"-1.4856E+02"}]
[5,{"v":5.6123821802558067E-7,"d":"5.6124E-07"},{"v":150,"d":"1.5000E+02"},{"v":-149.9999994387618,"d":"-1.5000E+02"}]
[6,{"v":9.26469018534798,"d":"9.2647E+00"},{"v":150,"d":"1.5000E+02"},{"v":-140.73530981465203,"d":"-1.4074E+02"}]
[7,{"v":0.014590951634474318,"d":"1.4591E-02"},{"v":150,"d":"1.5000E+02"},{"v":-149.98540904836554,"d":"-1.4999E+02"}]
[8,{"v":12.573074730417709,"d":"1.2573E+01"},{"v":150,"d":"1.5000E+02"},{"v":-137.42692526958228,"d":"-1.3743E+02"}]
[9,{"v":1.084645450021144E-3,"d":"1.0846E-03"},{"v":150,"d":"1.5000E+02"},{"v":-149.99891535454998,"d":"-1.5000E+02"}]
[10,{"v":0.6920480337946705,"d":"6.9205E-01"},{"v":150,"d":"1.5000E+02"},{"v":-149.30795196620534,"d":"-1.4931E+02"}]
[11,{"v":1.2402966201718222,"d":"1.2403E+00"},{"v":150,"d":"1.5000E+02"},{"v":-148.75970337982818,"d":"-1.4876E+02"}]
[12,{"v":0.16688649204702238,"d":"1.6689E-01"},{"v":150,"d":"1.5000E+02"},{"v":-149.833113507953,"d":"-1.4983E+02"}]
[13,{"v":0.00859605006096517,"d":"8.5961E-03"},{"v":150,"d":"1.5000E+02"},{"v":-149.99140394993904,"d":"-1.4999E+02"}]
[14,{"v":2.037438140580552,"d":"2.0374E+00"},{"v":150,"d":"1.5000E+02"},{"v":-147.96256185941945,"d":"-1.4796E+02"}]
[15,{"v":0.04523609792488,"d":"4.5236E-02"},{"v":150,"d":"1.5000E+02"},{"v":-149.95476390207511,"d":"-1.4995E+02"}]
[16,{"v":0.29734695199042704,"d":"2.9735E-01"},{"v":150,"d":"1.5000E+02"},{"v":-149.70265304800958,"d":"-1.4970E+02"}]
[17,{"v":0.0637131566309,"d":"6.3713E-02"},{"v":150,"d":"1.5000E+02"},{"v":-149.9362868433691,"d":"-1.4994E+02"}]
[18,{"v":1.0800113329717893,"d":"1.0800E+00"},{"v":150,"d":"1.5000E+02"},{"v":-148.9199886670282,"d":"-1.4892E+02"}]
[19,{"v":4.3855112332780862E-6,"d":"4.3855E-06"},{"v":150,"d":"1.5000E+02"},{"v":-149.99999561448877,"d":"-1.5000E+02"}]
[20,{"v":0.6903649039805627,"d":"6.9036E-01"},{"v":150,"d":"1.5000E+02"},{"v":-149.30963509601943,"d":"-1.4931E+02"}]
[21,{"v":0.030977708603665277,"d":"3.0978E-02"},{"v":150,"d":"1.5000E+02"},{"v":-149.96902229139633,"d":"-1.4997E+02"}]
[22,{"v":1.4266720955435914,"d":"1.4267E+00"},{"v":150,"d":"1.5000E+02"},{"v":-148.57332790445642,"d":"-1.4857E+02"}]
[23,{"v":0.7157178351266229,"d":"7.1572E-01"},{"v":150,"d":"1.5000E+02"},{"v":-149.2842821648734,"d":"-1.4928E+02"}]
[24,{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"}]
[25,{"v":1.7999521521299424,"d":"1.8000E+00"},{"v":150,"d":"1.5000E+02"},{"v":-148.20004784787005,"d":"-1.4820E+02"}]
[]
["From the simulation, we can conclude that the particulate standard is not exceeded at any of the receptor locations.  In this case it is unnecessary to run an optimization model as the cost of meeting the standards is $0/day"]

{"sheet":"Example 3","index":21,"n_rows":80,"n_cols":7,"rows_kept":80,"merged":[[2,0,3,3],[5,0,5,3],[18,0,18,3],[34,0,34,3],[79,0,79,5]]}
["Example 3"]
["New York NOX Pollution"]
["Smog is a type of air pollution typically found in urban areas that results from vehicle emissions and industrial processes.  There are several different components of smog including sulfur dioxide, nitrogen oxides (NOX), volatile organic carbons (VOCs), and ozone.  In this example we are going to focus on nitrogen oxide emissions from 8 sources in an urban NY area.  "]
[]
[]
["Many urban areas of NY have NOX pollution problems. In our area of interest NOX is emitted from eight major sources in the area. The sources include natural gas turbines, gas and diesel engines, and fuel oil consumption.  Emissions of NOX from the eight sources are given below."]
[]
["Sources","Emissions (kg/day)","Stack Height (m)","Cost of Removal ($/kg)"]
[1,{"$f":"4.08*3000/2","v":6120},18,0.36]
[2,{"$f":"0.32*2000/2","v":320},27,0.47]
[3,{"$f":"47*60","v":2820},24,0.16]
[4,{"$f":"0.11*24*5000/2","v":6600},15,0.36]
[5,{"$f":"0.011*24*45000/2","v":5940},16,0.44]
[6,{"$f":"0.031*24*30000/2","v":11160},15,0.27]
[7,{"$f":"0.32*250/2","v":40},20,0.51]
[8,{"$f":"4.08*95/2","v":193.8},18,0.22]
[]
[]
["A preliminary assessment has identified the \"critical\" weather conditions in the area as a 1.3 m/sec wind speed on a clear night . Ten ground level receptors have been selected as places where health effects are most important: schools, hospitals, and nursing homes. The national ambient air quality standard for NOX is 53 ug/m3.  Locations of sources and receptors in an X-Y coordinate system with (0,0) origin are given below. The X axis is parallel to the wind direction. Determine which sources need to decrease their emissions in order to meet the standard and how much it will cost to do this."]
[]
["Source","(X,Y) (km)","Receptor","(X,Y) (km)"]
[1,"31,26",1,"4,10"]
[2,"37,40",2,"7,32"]
[3,"44,18",3,"40,15"]
[4,"8,18",4,"6,33"]
[5,"21,3",5,"34,29"]
[6,"35,39",6,"4,25"]
[7,"2,13",7,"16,9"]
[8,"0,12",8,"15,40"]
[null,null,9,"1,28"]
[null,null,10,"40,2"]
[]
[]
["SOLUTION:"]
["After inputting the above information into the model, we ran a simulation to see if the maximum concentration was being exceeded at any receptor.  We found that receptor 10 had a concentration that was above the acceptable limit (as shown below)."]
[]
[]
[]
["Receptor","Original Concentration (ug/m3)","Maximum Concentration at Receptor (ug/m3)","Concentration Difference (ug/m3)"]
[1,{"v":1.612782674030092e-27,"d":"1.6128E-27"},{"v":53,"d":"5.3000E+01"},{"v":-53,"d":"-5.3000E+01"}]
[2,{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"}]
[3,{"v":4.10087229497035,"d":"4.1009E+00"},{"v":53,"d":"5.3000E+01"},{"v":-48.89912770502965,"d":"-4.8899E+01"}]
[4,{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"}]
[5,{"v":6.746679682077118E-29,"d":"6.7467E-29"},{"v":53,"d":"5.3000E+01"},{"v":-53,"d":"-5.3000E+01"}]
[6,{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"}]
[7,{"v":3.8545540064805279E-5,"d":"3.8546E-05"},{"v":53,"d":"5.3000E+01"},{"v":-52.999961454459935,"d":"-5.3000E+01"}]
[8,{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"}]
[9,{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"},{"v":0,"d":"0.0000E+00"}]
[10,{"v":84.2247238478932,"d":"8.4225E+01"},{"v":53,"d":"5.3000E+01"},{"v":31.224723847893202,"d":"3.1225E+01"}]
[]
[]
["We then went back to the input tab where we ran an optimization model.  The results from this were as follows:"]
[]
["Total Cost of Removal"]
[null,{"v":968.9427821246773,"d":"$968.94"},"per day"]
[]
[]
["Source","Original Emissions (kg/day)","Cost of Removal ($/kg)","New Emissions (kg/day)","Emissions Removed (kg/day)","Total Cost of Removal ($)","Percent Reduction"]
[1,{"v":6120,"d":"6120.00"},0.36,{"v":6120,"d":"6120.00"},{"v":0,"d":"0.00"},{"v":0,"d":"$0.00"},{"v":0,"d":"0.00%"}]
[2,{"v":320,"d":"320.00"},0.47,{"v":320,"d":"320.00"},{"v":0,"d":"0.00"},{"v":0,"d":"$0.00"},{"v":0,"d":"0.00%"}]
[3,{"v":2820,"d":"2820.00"},0.16,{"v":2820,"d":"2820.00"},{"v":0,"d":"0.00"},{"v":0,"d":"$0.00"},{"v":0,"d":"0.00%"}]
[4,{"v":6600,"d":"6600.00"},0.36,{"v":6600,"d":"6600.00"},{"v":0,"d":"0.00"},{"v":0,"d":"$0.00"},{"v":0,"d":"0.00%"}]
[5,{"v":5940,"d":"5940.00"},0.44,{"v":3737.8573133530062,"d":"3737.86"},{"v":2202.1426866469938,"d":"2202.14"},{"v":968.9427821246773,"d":"$968.94"},{"v":0.37073109202811344,"d":"37.07%"}]
[6,{"v":11160,"d":"11160.00"},0.27,{"v":11160,"d":"11160.00"},{"v":0,"d":"0.00"},{"v":0,"d":"$0.00"},{"v":0,"d":"0.00%"}]
[7,{"v":40,"d":"40.00"},0.51,{"v":40,"d":"40.00"},{"v":0,"d":"0.00"},{"v":0,"d":"$0.00"},{"v":0,"d":"0.00%"}]
[8,{"v":193.8,"d":"193.80"},0.22,{"v":193.8,"d":"193.80"},{"v":0,"d":"0.00"},{"v":0,"d":"$0.00"},{"v":0,"d":"0.00%"}]
[]
[]
["Receptor","Concentration after Emissions Reduction (ug/m3)"]
[1,1.612782674030092e-27]
[2,0]
[3,4.10087229497035]
[4,0]
[5,6.746679682077118E-29]
[6,0]
[7,3.8545540064805279E-5]
[8,0]
[9,0]
[10,52.99999999999999]
["For this problem, we determined that source 5 needed to reduce their emissions by 37% to 3738 kg/day in order to meet the NOX concentration limits."]