Asked by Magdalena

A company separates tin, copper, and kryptonite from ore by the flotation separation process, which has three steps: oiling, mixing, and separation. These steps must be applied for 2, 3, and 1 hour respectively to produce one unit of tin; 2, 2, and 1 hour respectively to produce one unit of copper; and 1, 1, 3 hours respectively to produce one unit of kryptonite. Because of limited access to equipment, the oiling and separation phases can each be in operation for a maximum of 10 hours per week, and the mixing process can be in operation for a maximum of 13 hours per week (note the order in which the phases appear in this sentence). The company makes a profit of $35 per unit of tin, $45 per unit of copper, and $40 per unit of kryptonite. Assuming that the demand for each metal is unlimited, how many units of each metal should the company produce each week to maximize its profit?