A company separates iron, zinc, and kryptonite from ore by the floatation separa

Question

A company separates iron, zinc, and kryptonite from ore by the floatation separation process, which has three steps: oiling, mixing, and separation. These steps must be applied for 2, 4, and 1 hour respectively to produce one unit of iron; 2, 2, and 1 hour respectively to produce one unit of zinc; 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 14 hours per week, and the mixing process can be in operation for a maximum of 15 hours per week. The company makes a profit of $25 per unit of iron, $40 per unit of zinc, and $30 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?

Enter the linear optimization problem which represents this situation.

Number of units of iron =  

Number of units of zinc =  

Number of units of kryptonite =

Explanation / Answer

Let no of units of Iron be x (profit is $25)

Let no of units of Zinc be y (profit is $40)

Let no of units of Kryptonite be z (profit is $30)

We have to maximize Zinc because of its maximum profit(Also Zinc has minimum number of operating hours i.e 5)

hence, we will be producing 6 Zinc and 2 Kryptonite

Therefore profit = 6*40 + 2*30 = 300

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