M&D Chemicals produces two products, A31 and C42 sold as raw materals to compaines manufacturing bath soaps, laundry detergents, and other soap products. Based on an analysis of current inventory levels and potential and other soap products. Based on an analysis of current inventory levels and potential demand for the coming month, M&D's managers have specified that the total production of products A31 and C42 combined must be at least 350 gallons. Also, a major customer's order for 100 gallons of A31 must be satisfied. A31 requires 2 hours of processing time per gallon, and C42 requires 1 hour; 600 hours of processing time are available in the coming month. In addition, producing A31 and C42 requires a special catalytic agent. A31 requires 0.1 pound and C42 requires 0.2 pounds. M&D has 50 pounds of the catalytic. Finally, production costs are $20 per gallon for product 1 and $30 per gallon for product 2.
a. Write a linear program that minimizes cost.
b. What is the optimal production cost and the total amounts of A31 and C42?
c. M&D wants to sell the remaining pounds of the catalytic agent at a price of $100. How much money will be generated from the sell?