Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P1  and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1  by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts.  Are the LP assumptions (proportionality, additivity, divisibility) reasonable in this problem? b. Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what happens to the amount of waste processed at the three factories and the total cost if both requirements (currently 125 and 175 tons, respectively) are increased by the same percentage. Revise your model so that you can use SolverTable to investigate these changes when the percentage increase varies from 10% to 100% in increments of 10%. Do the amount processed at the three factories and the total cost change in a linear manner?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Is my solution correct and did I fully answer the questions? (see attachment for my solution)

Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of Pby 0.10 ton and the amount of Pby 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of Pby 0.20 ton and the amount of Pby 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P by 0.40 ton and the amount of Pby 0.50 ton. The state wants to reduce the amount of Pin the river by at least 125 tons and the amount of P2 by at least 175 tons.

a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts.  Are the LP assumptions (proportionality, additivity, divisibility) reasonable in this problem?

b. Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what happens to the amount of waste processed at the three factories and the total cost if both requirements (currently 125 and 175 tons, respectively) are increased by the same percentage. Revise your model so that you can use SolverTable to investigate these changes when the percentage increase varies from 10% to 100% in increments of 10%. Do the amount processed at the three factories and the total cost change in a linear manner?

The image displays an Excel spreadsheet aimed at analyzing the processing and cost management of river pollutants, as well as the reduction of said pollutants. The spreadsheet seems to be used for an educational purpose to teach students about environmental management and optimization.

### River Pollutants Analysis Spreadsheet

#### Column Headers and Key Information (A1 - H16):
- **River pollutants:** (Title of the spreadsheet)
- **Cost per Ton for F1, F2, and F3:** Processed costs per ton displayed in cells B3 (57.69230769), C3 (0), and D3 (298.0769231) respectively.
- **Total Cost:** Displayed in cells E3 and F3.
  - The total cost value is 980769.231.
  
#### Factory Information and Pollution Details (A4 - H8):
- **Pollutants processed by the respective factories** are displayed in columns B6 to D7 for pollutants 1 and 2. 
  - **Pollutant 1:**
    - F1: 0.1
    - F2: 0.2
    - F3: 0.4
  - **Pollutant 2:**
    - F1: 0.45
    - F2: 0.25   
    - F3: 0.5

#### Reduction Requirements (E8 - H10):
- **Reduction requirement values for pollutants:** 
  - For Pollutant 1: 125 (cell H9)
  - For Pollutant 2: 175 (cell H10)
  
#### Sensitivity Analysis Data (A12 - H44):
  
- **% change in requirements:** Cells A12 to F23 analyze the changes in requirements processed by F1, F2, and F3.
- **Processed data with varying % changes:**
  - Example:
    - 10% change shows values 57.69 for Processed 1, 0.00 for Processed 2, and 298.08 for Processed 3.
    - Similarly, different percentage changes show corresponding processed and cost values.
#### Differences in Data (A25 - H44):

- **Detailed differences from 10% to 100% changes:** 
  - Each 10% change in requirements is detailed from cells A25 through H44.
  - Observations:
    - For every 10% increase in
Transcribed Image Text:The image displays an Excel spreadsheet aimed at analyzing the processing and cost management of river pollutants, as well as the reduction of said pollutants. The spreadsheet seems to be used for an educational purpose to teach students about environmental management and optimization. ### River Pollutants Analysis Spreadsheet #### Column Headers and Key Information (A1 - H16): - **River pollutants:** (Title of the spreadsheet) - **Cost per Ton for F1, F2, and F3:** Processed costs per ton displayed in cells B3 (57.69230769), C3 (0), and D3 (298.0769231) respectively. - **Total Cost:** Displayed in cells E3 and F3. - The total cost value is 980769.231. #### Factory Information and Pollution Details (A4 - H8): - **Pollutants processed by the respective factories** are displayed in columns B6 to D7 for pollutants 1 and 2. - **Pollutant 1:** - F1: 0.1 - F2: 0.2 - F3: 0.4 - **Pollutant 2:** - F1: 0.45 - F2: 0.25 - F3: 0.5 #### Reduction Requirements (E8 - H10): - **Reduction requirement values for pollutants:** - For Pollutant 1: 125 (cell H9) - For Pollutant 2: 175 (cell H10) #### Sensitivity Analysis Data (A12 - H44): - **% change in requirements:** Cells A12 to F23 analyze the changes in requirements processed by F1, F2, and F3. - **Processed data with varying % changes:** - Example: - 10% change shows values 57.69 for Processed 1, 0.00 for Processed 2, and 298.08 for Processed 3. - Similarly, different percentage changes show corresponding processed and cost values. #### Differences in Data (A25 - H44): - **Detailed differences from 10% to 100% changes:** - Each 10% change in requirements is detailed from cells A25 through H44. - Observations: - For every 10% increase in
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