Question

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Steel Company manufactures two kinds of wrought-iron rails: Model \(\mathrm{E}\) (the elegant) and Model D (the distinctive). Model E rails sell for \(\$ 59\) and cost \(\$ 50\) to make, whereas Model D rails sell for \(\$ 48\) and cost \(\$ 41\) to make. To make one Model \(E\) rail requires 2 hours on Machine \(A, 1\) hour on Machine \(B,\) and 4 hours on Machine \(C\). On the other hand, to make one Model \(D\) rail requires 1 hour on \(A, 2\) hours on \(B,\) and 5 hours on C. Production scheduling indicates that during the coming week Machine A will be available for at most

30 hours, Machine \(\mathrm{B}\) for at most 24 hours, and Machine \(\mathrm{C}\) 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. Calculate the maximum profit.