M&D Chemicals produces two products sold as raw materials to companies manufacturing bath soaps, laundry detergents, 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 1 and 2 combined must be at least 350 gallons. Also, a major customer's order for 125 gallons of product 1 must be satisfied. Product 1 requires 2 hours of processing time per gallon, and product 2 requires 1 hour; 600 hours of processing time are available in the coming month. Production costs are $2 per gallon for product 1 and $3 per gallon for product 2.
a. Determine the production quantities that will satisfy the specified requirements at minimum cost.
b. What is the total product cost?
c. Identify the amount of any surplus production.