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A manufacturer of engine parts produces valves and pistons at its main plant. Both parts are processed by the Machining Department and by the Finishing Department. Each valve requires 0.4 hours of machining time and 0.3 hours of finishing time, and each piston requires 0.3 hours of machining and 0.5 hours of finishing. The production process also requires 2 pounds of steel for each part.

A manufacturer of engine parts produces valves and pistons at its main plant. Both parts are processed by the Machining Department and by the Finishing Department. Each valve requires 0.4 hours of machining time and 0.3 hours of finishing time, and each piston requires 0.3 hours of machining and 0.5 hours of finishing. The production process also requires 2 pounds of steel for each part.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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Problem 1: A manufacturer of engine parts produces valves and pistons at its main plant. Both parts are processed by the Machining Department and by the Finishing Department. Each valve requires 0.4 hours of machining time and 0.3 hours of finishing time, and each piston requires 0.3 hours of machining and 0.5 hours of finishing. The production process also requires 2 pounds of steel for each part. In drawing up a schedule for the coming month the plant manager knows that 300 hours of production time will be available in the Machining Department and 400 hours will be available in the Finishing Department. In addition, existing contracts provide for the delivery of 1800 pounds of steel during the month. The market for valves and pistons is competitive, and the company can sell all the parts it produces during the month. At current prices the gross profit on each valve sold is OR3, while for each piston sold the gross profit is OR4. The plant manager would like to find a production plan for the month that will maximise profits. Determine the optimal plan and the maximum possible profit.
Transcribed Image Text:Problem 1: A manufacturer of engine parts produces valves and pistons at its main plant. Both parts are processed by the Machining Department and by the Finishing Department. Each valve requires 0.4 hours of machining time and 0.3 hours of finishing time, and each piston requires 0.3 hours of machining and 0.5 hours of finishing. The production process also requires 2 pounds of steel for each part. In drawing up a schedule for the coming month the plant manager knows that 300 hours of production time will be available in the Machining Department and 400 hours will be available in the Finishing Department. In addition, existing contracts provide for the delivery of 1800 pounds of steel during the month. The market for valves and pistons is competitive, and the company can sell all the parts it produces during the month. At current prices the gross profit on each valve sold is OR3, while for each piston sold the gross profit is OR4. The plant manager would like to find a production plan for the month that will maximise profits. Determine the optimal plan and the maximum possible profit.
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