Fill in the blanks in each of the.

If the feasible region for a LPP is _________, then the optimal value of the objective function Z = ax + by may or may not exist.

Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px+qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is

Using the method of integration, find the area of the region bounded by the following lines:

5x - 2y - 10 = 0

x + y - 9 = 0

2x - 5y - 4 = 0

Refer to Exercise 27. (Maximum value of Z + Minimum value of Z) is equal to

A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below :

One kg of food X costs ₹16 and one kg of food Y costs ₹ 20. Find the least cost of the mixture which will produce the required diet?

A merchant plans to sell two types of personal computers — a desktop model and a portable model that will cost 25,000 and 40,000 respectively. He estimates that the total monthly demand for computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than ` 70 lakhs and his profit on the desktop model is ` 4,500 and on the portable model is 5,000. Make an L.P.P. and solve it graphically.

A dietician wishes to mix two types of foods in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 units/kg of vitamin C while Food II contains 1unit/kg of vitamin A and 2 units/kg of vitamin C. It costs ₹ 5 per kg to purchase Food I and 7 per kg to purchase Food II. Determine the minimum cost of such a mixture. Formulate the above as a LPP and solve it graphically.

Maximise and Minimise Z = 3x – 4y

subject to x – 2y ≤ 0

– 3x + y ≤ 4

x – y ≤ 6

x, y ≥ 0