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.