Answer to Question #305125 in Management for hella

Question

Consider the following product mix problem:

Three machine shops A, B, C produces three types of products X, Y, Z respectively. Each product involves operation of each of the machine shops. The time required for each operation on various products is given as follows:

Machine shops

Products                    A      B       C               Profit per unit X                                10      7        2                Birr 12 Y                                  2      3        4                Birr 3 Z                                  1      2        1                Birr 1 Available Hours       100   77       80 Make the Mathematical model of the above primal problem to maximise the profit and then make the dual problem.

Answer 1

1 2 x1 + 2x2 + x3 ≤ 24,

x1 + 2x2 + 4x3 ≤ 60,

(1) x1 ≥ 0,

x2 ≥ 0,

x3 ≥ 0.