If the number of units of iron, lead, and kryptonite are x,y,z respectively, then we have to maximize
p = 55x+70y+60z
subject to
3x+3y+z <= 22
4x+3y+z <= 22
x+y+4z <= 23
Now use your favorite linear programming method
A company separates iron, lead, and kryptonite from ore by the floatation separation process, which has three steps: oiling, mixing, and separation. These steps must be applied for 3, 4, and 1 hour respectively to produce one unit of iron; 3, 3, and 1 hour respectively to produce one unit of lead; and 1, 1, 4 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 22 hours per week, and the mixing process can be in operation for a maximum of 23 hours per week. The company makes a profit of $55 per unit of iron, $70 per unit of lead, and $60 per unit of kryptonite. Assuming that the demaind for each metal is unlimited, how many units of each metal should the company produce each week to maximize its profit?
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