Question

Because of new federal regulations on pollution, a chemical plant introduced a new, more expensive process to supplement or replace an older process used in the production of a particular chemical. The older process emitted 20grams of sulfur dioxide and 40 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5grams of sulfur dioxide and 20 grams of particulate matter for each gallon produced. The company makes a profit of 60 cents per gallon and 20 cents per gallon on the old and new processes, respectively.

a) If the government allows the plant to emit no more than 16,000 grams of sulfur dioxide and 30,000 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? What is maximum daily profit?

b) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 11,500 grams daily and all other data remain unchanged.

c) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 7,200 grams daily and all other data remain unchanged.

Answer 1

When the limitation on production of both sulfur dioxide and Particulate matter is given, the number of gallons produced is selected such that maximum production of sulfur dioxide and Particulate matter is not exceeded.