M&D Chemicals produces two products that are sold as raw materials to companies manu- facturing 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.

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Formulate an LP for this minimization problem

M&D Chemicals produces two products that are sold as raw materials to companies manu-
facturing 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.
Transcribed Image Text:M&D Chemicals produces two products that are sold as raw materials to companies manu- facturing 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.
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