Company supplies castings to variety of customers

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The Middletown Steel Company supplies castings to a variety of customers. It plans to devote the next week of production to just two of these customers: A Ltd. and B Ltd. Middletown uses a combination of pure steel and scrap metal to fulfill its orders and has 400 pounds of pure steel and 360 pounds of scrap metal in stock. The pure steel costs Middletown $6 per pound and the scrap metal costs Middletown $3 per pound. Pure steel requires 3 hours of processing time per pound to process into a casting, while scrap metal requires only 2 hours of processing time per pound to process into a casting. The total available processing time in the week is 2000 hours. The castings for A Ltd. each require 5 pounds of metal, with a quality restriction that limits the ratio of scrap metal to pure steel to a maximum of 5/7. A Ltd. has ordered 30 castings at a price of $50 each. The castings for B Ltd. each require 8 pounds of metal, with a quality control restriction that limits the ratio of scrap metal to pure steel to a maximum of 2/3. B Ltd. has ordered 40 castings at a price of $80 each.

Formulate an LP that can be used to maximize Middletown’s profit over the next week.

Reference no: EM132222963

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