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XYZ Steel Company manufactures two kinds of wrought-iron rails: Model E, the elegant, and Model D, the distinctive. Model E rails sell for $99 and cost $90 to make, whereas Model D rails sell for $88 and cost $81 to make. To make one Model E rail requires two hours on Machine A, one hour on Machine B, and four hours on Machine C. To make one Model D rail requires one hour on A, two hours on B, and five hours on C. Pro- duction scheduling indicates that during the coming week Machine A will be avail- able for at most 30 hours, Machine B for at most 24 hours, and Machine C for at most 72 hours. Find the number of each kind of rail to be made in the coming week in order for the company to maximize its profit. What is this maximum profit? At the maximum, which machines, if any, are not fully utilized?

XYZ Steel Company manufactures two kinds of wrought-iron rails: Model E, the elegant, and Model D, the distinctive. Model E rails sell for $99 and cost $90 to make, whereas Model D rails sell for $88 and cost $81 to make. To make one Model E rail requires two hours on Machine A, one hour on Machine B, and four hours on Machine C. To make one Model D rail requires one hour on A, two hours on B, and five hours on C. Pro- duction scheduling indicates that during the coming week Machine A will be avail- able for at most 30 hours, Machine B for at most 24 hours, and Machine C for at most 72 hours. Find the number of each kind of rail to be made in the coming week in order for the company to maximize its profit. What is this maximum profit? At the maximum, which machines, if any, are not fully utilized?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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XYZ Steel Company manufactures two kinds of wrought-iron rails: Model E, the elegant, and Model D, the distinctive. Model E rails sell for $99 and cost $90 to make, whereas Model D rails sell for $88 and cost $81 to make. To make one Model E rail requires two hours on Machine A, one hour on Machine B, and four hours on Machine C. To make one Model D rail requires one hour on A, two hours on B, and five hours on C. Pro- duction scheduling indicates that during the coming week Machine A will be avail- able for at most 30 hours, Machine B for at most 24 hours, and Machine C for at most 72 hours. Find the number of each kind of rail to be made in the coming week in order for the company to maximize its profit. What is this maximum profit? At the maximum, which machines, if any, are not fully utilized?
Transcribed Image Text:XYZ Steel Company manufactures two kinds of wrought-iron rails: Model E, the elegant, and Model D, the distinctive. Model E rails sell for $99 and cost $90 to make, whereas Model D rails sell for $88 and cost $81 to make. To make one Model E rail requires two hours on Machine A, one hour on Machine B, and four hours on Machine C. To make one Model D rail requires one hour on A, two hours on B, and five hours on C. Pro- duction scheduling indicates that during the coming week Machine A will be avail- able for at most 30 hours, Machine B for at most 24 hours, and Machine C for at most 72 hours. Find the number of each kind of rail to be made in the coming week in order for the company to maximize its profit. What is this maximum profit? At the maximum, which machines, if any, are not fully utilized?
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