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A small firm makes three similar products, which all follow the same three-step process, consisting of milling, inspection, and drilling. Product X requires 12 minutes of milling, 5 minutes for inspection, and 10 minutes of drilling per unit; product Y requires 9 minutes of milling, 6 minutes of inspection, and 7 minutes of drilling per unit; and product Z requires 8 minutes of milling, 4 minutes for inspection, and 16 minutes of drilling.
The department has 18 hours available during the next period for milling, 19 hours for inspection, and 15 hours for drilling. Product X contributes $2.40 per unit to profit, Y contributes $2.50 per unit, and Z contributes $3.00 per unit. Because the demands for X and Y are highly correlated, it is determined that the ratio of quantities of X to Y should be 1:2.
The firm would like to determine what mix of each of the three products to produce so as to maximize profit. Formulate this problem as a linear program and solve it.
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