A factory along River Pra emits pollutants into the river through its three stages of processing raw

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Question:

A factory along River Pra emits pollutants into the river through its three stages of processing raw materials. Pollution of the river can however be reduced if the waste is processed and recycled properly. The harm is caused by two major pollutants, pollutant X and pollutant Y. A recycling plant has been contracted by the company to assess the pollution and provide an optimum means of reducing the impact of the pollution at the barest cost.

The recycling plant has noted that it will cost 600 credits to process a ton of waste at stage A of the processing, and each ton of waste processed at this stage reduces the amount of pollutant X by 10% and pollutant Y by 45%. At stage B, it will cost 400 credits to process a ton of waste and each ton processed will reduce pollutant X emission by 20% and that of pollutant Y by 25%. It will also cost 800 credits to process a ton of waste at stage C of processing and this will reduce emission of pollutant X by 40% and that of Y by 30%. The Environmental Protection Agency has warned that the company must reduce emission of pollutant X by at least 30 tons and that of Y by no less than 40 tons or face a total shut down. The company would like to carry out this task at the barest minimum cost.

Questions

a. Identify the decision variables for this problem

b. Write down a mathematical model to meet the objective of the company. In your own words, briefly explain what the objective function seeks to achieve.

c. Write down the various mathematical functions or inequalities that represent the requirements of the EPA.

d. Solve this problem using the Excel solver

e. In your own words, briefly explain the course of action that must be taken by the company based on the results of your modelling (take into account the slack or surplus variables, shadow prices and other values from the solver report that may deem necessary).