19. A diet conscious housewife wishes to ensure certain minimum intake of vitamins A, B and C for the family. The minimum daily needs of vitamins A, B and C for the family are 60, 40 and 32 units, respectively. For the supply of these vitamins, the housewife relies on two fresh foods F 1 and F2• One unit of F1 contains 14, 10 and 4 units of vitamins A, Band C, respectively. One unit of F2 contains 4, 8 and 16 units of the three vitamins, respectively. F1 costs Rs 3 per unit and F2 Rs 2 perunit. The problem is how many units of each food the housewife should buy every day to keep her food bill as low as possible.

(a) Formulate it as a linear programming problem to minimise the total cost;

(b) Write the dual of the problem as formulated in

(a) and present the economic interpretation of the dual; and

(c) Solve the dual by using simplex method and read therefrom the answer to the primal.