A firm uses three machines in the manufacture of three products. Each unit of product A requires 3 hours on machine 1, 2 hours on machine II and one hour on machine Ill. Each unit of product B requires 4 hours on machine I, one hour on machine II and 3 hours on machine 111, while each unit of product C requires 2 hours on each of the three machines. The contribution margin of the three products is Rs 30, Rs 40 and Rs 35 per unit respectively. The machine hours available on three machines are 90, 54 and 93 respectively.

(i) Formulate the above problem as a linear programming problem.

(ii) Obtain optimal solution to the problem by using the simplex method. Which of the three products shall not by produced by the firm? Why?

(iii) Calculate the percentage of capacity utilisation in the optimal solution.

(iv) What are the shadow prices of the machine hours?

(v) Is the optimal solution degenerate?