A new pollution control law has been passed by the state legistature requiring manufactures to reduce pollution by 30%. A local agricultural by-product processing facility produced known emissions of three pollutants into the air that we'll call A, B, and C. Under the new state law, the plant is required to reduce emissions of A by at least 50 units, B by at least 75 units, and C by at least 100 units each year.

The company has access to two pollution abatement methods: (1) the use of air-scrubbers and (2) the use of a biological agent in the manufacturing process that will reduce emissions. Both methods can be used simultaneously with no diminished effectfor either. For each air scrubber that is used, the emission of the three pollutants will be reduced by 5, 10, and 20 units annually for A, B, and C. Each scrubber will cost $25,000 per year to own and operate. For each ton of biological neutralizing agent used in processing, the three pollutants will be reduced by 1, 4, and 5 units. The biological agent currently costs $1,500 per ton.

The manufacture's core policy is to continue generating output to meet the demand of its customers as it has for the past decade. It does not expect this demand to shift from where it was last year ($100 million product), with plant output excepted to be unchanged. Given the firm's commitment to maintain their level of output, the company must identify a plan thag will allow it to also comply with the new state regulation yet generate the greatest possible returns to its shareholders.

You need to formulate (but not solve) the LP model that will allow you to prescribe the best means to perform pollution abatement activities given the firm's desires and opportunities described. Specifically, you must identify and define (a) the decision variabled for your model and express algebraically (b) the objective function and (c) any relevant constraints.