Linear Programm...

Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and

Minimize Z = 3x + 5y such that x + 3y ≥3, x + y ≥2, x, y ≥0.

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?

Maximise the function Z = 11x + 7y, subject to the constraints: x ≤3, y ≤2,x ≥0, y ≥0.

The feasible region for a LPP is shown in Figure. Evaluate Z = 4x + y at each of the corner points of this region. Find the minimum value of Z, if it exists

A maximum or a minimum may not exist for a linear programming problem if

Maximize Z = 3x + 2y subject to x + 2y ≤10, 3x + y ≤15, x, y ≥0.

A merchant plans to sell two types of personal computers –a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of 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 Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

Minimise Z = 13x –15y subject to the constraints : x + y ≤7, 2x –3y + 6 ≥0 , x ≥0, y ≥0.

In Figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y

In Corner point method for solving a linear programming problem the first step is to

Minimize Z = x + 2y subject to 2x + y ≥3, x + 2y ≥6, x, y ≥0.

A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

Maximize Z = 100x + 120y , subject to constraints 2x + 3y ≤30, 3x + y ≤17, x ≥0, y ≥0.

Determine the minimum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure above.