M&D Chemicals produces two products that are sold as raw materials to companies that manufacture bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demand for the coming month, M&D’s management specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customer’s order for 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon, and product B requires 1 hour of processing time per gallon. For the coming month, 600 hours of processing time are available. M&D’s objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 per gallon for product B.
Linear program for the M&D Chemicals problem:
Min 2A + 3B
s.t. 1A ≥ 125 Demand for product A
1A + 1B ≥ 350 Total production
2A + 1B ≤ 600 Processing time
A, B ≥ 0
If the combined production for products a abs he must total at least 400, what is the minimum total cost?