Ouestion (2): company produces two lines of its products, the super and regular.

Question

Ouestion (2): company produces two lines of its products, the super and regular. Resource requirements and the available resources for production are given in the following table: Production Line Profit contributiol Assembly time Paint time Regular Super Available Resource 0.8 hrs 0.9 hrs 700 hrs Inspection time 0.2 hrs 0.2 hrs 500 hrs S70 1.2 hrs 1.6 hrs l800 hrs S50 so Regular customers will demand at least 150 units of regular line and 50 of super. Formulate the LP problem that will determine the optimal solution.

Explanation / Answer

Let Z = Profit, X1 = number of units of regular line, X2 = number of units of super line.

Our objective function is to:
Maximise Z = (70 * X1) + (50 * X2).

The constraints are:
Assembly time -> (1.2 * X1) + (1.6 * X2) <= 1800
Paint time -> (0.8 * X1) + (0.9 * X2) <= 700
Inspection time -> (0.2 * X1) + (0.2 * X2) <= 500

Further, X1 >= 150 and X2 >= 50.

Our LP problem is then:
Max Z = (70 * X1) + (50 * X2)
subject to
(1.2 * X1) + (1.6 * X2) <= 1800
(0.8 * X1) + (0.9 * X2) <= 700
(0.2 * X1) + (0.2 * X2) <= 500
X1 >= 150, X2 >= 50.

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