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(a) A company sells three different products X, Y and Z. The company makes a profit of Rs. 35, Rs. 50 and Rs. 60 per unit on products X, Y and Z respectively. The three products are produced in a common production process and are sold in three different markets. The total production process has a total capacity of 20000 man-hours. It takes two hours to produce a unit of X, three hours to produce a unit of Y and two hours to produce a unit of Z.
The market has been surveyed and it is found that the maximum units of X, Y and Z that can be sold are 12000, 8000 and 6000 respectively. Explain fully how you would formulate a linear programming model for this problem.
(b) A product mix problem can be formulated mathematically as follows:
Max Z = 100x1 + 75x2
subject to the constraints
5x1 + 10 x2 ≤ 1500 8x1 + 5x2 ≤ 1200 x1 ≤ 300 and x2 ≤ 400 x1 ≥ 0, x2 ≥ 0
Solve the above product mix problem using graphical method.
(c) Explain briefly the term ‘sensitivity analysis'.
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