Question

a) A firm produces three products A, B and C. It uses two types of raw materials I and II of which 5000 and 7500 units, respectively, are available. The raw material requirements per unit of the products are given below : Raw Material Requirement per unit of product A B C I 3 4 5 II 5 3 5 The labour time for each unit of Product A is twice as that of Product B and three times that of Product C. The entire labour force of the firm can produce the equivalent of 3000 units. The minimum demand for the three products are 600, 650 and 500 units respectively. Also, the ratio of the number of units produced must be equal to 2 : 3 : 4. Assuming the profits per unit of A, B and C are 50, 50 and 80, respectively, formulate the problem as a linear programming problem in order to determine the number of units of each product which will maximise the profit.

Answer 1

Answer:

Let, x1 = number of units produced by A x2 = number of units produced by B x3 = number of units produced by C Profit per unit of product A = Rs 50 Profit per unit of product B = Rs 50 Profit per unit

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