(a) Formulate a linear optimization model that can be used by M&D′ s to satisfy the specified requirements at a minimum total production cost. (b) What are the optimal production quantities?
M&D Chemicals produces two products that are sold as raw materials to companies
manufacturing 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 at least 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. Production costs are $2 per gallon for product
A and $3 per gallon for product B.
(a) Formulate a linear optimization model that can be used by M&D′
s to satisfy
the specified requirements at a minimum total production cost.
(b) What are the optimal production quantities?
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