A company uses three machines, I, II, and III to produce items X, Y, and Z. The

Chapter 8, Problem 10

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A company uses three machines, I, II, and III to produce items X, Y, and Z. The production of each item involves the use of more than one machine. It takes 2 minutes on I and 4 minutes on II to manufacture a single X. It takes 3 minutes on I and 6 minutes on III to manufacture a Y. It takes 1 minute on I, 2 minutes on II, and 3 minutes on III to manufacture a Z. The total time available on each machine per day is 6 hours. The profits are $10, $8, and $12 on each of X, Y, and Z, respectively. How should the company allocate the production times on the machines in order to maximize total profit?

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