Linear Programming Problem (L.P.P.)

State whether the following is True or False :

Saina wants to invest at most ₹ 24000 in bonds and fixed deposits. Mathematically this constraints is written as x + y ≤ 24000 where x is investment in bond and y is in fixed deposits.

A manufacturer produces bulbs and tubes. Each of these must be processed through two machines M₁ and M₂. A package of bulbs requires 1 hour of work on Machine M₁ and 3 hours of work on M₂. A package of tubes requires 2 hours on Machine M₁ and 4 hours on Machine M₂. He earns a profit of ₹ 13.5 per package of bulbs and ₹ 55 per package of tubes. If maximum availability of Machine M₁ is 10 hours and that of Machine M₂ is 12 hours, then formulate the L.P.P. to maximize the profit.

Solve the following L.P.P. by graphical method:

Maximize: Z = 4x + 6y

Subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.

Food F₁ contains 2, 6, 1 units and food F₂ contains 1, 1, 3 units of proteins, carbohydrates, fats respectively per kg. 8, 12 and 9 units of proteins, carbohydrates and fats is the weekly minimum requirement for a person. The cost of food F₁ is Rs. 85 and food F₂ is Rs. 40 per kg. Formulate the L.P.P. to minimize the cost.

Solve the following linear programming problem graphically.

Minimize Z = 200x₁ + 500x₂ subject to the constraints: x₁ + 2x₂ ≥ 10; 3x₁ + 4x₂ ≤ 24 and x₁ ≥ 0, x₂ ≥ 0.

Fill in the blank :

A dish washing machine holds up to 40 pieces of large crockery (x) This constraint is given by_______.

A company produces mixers and food processors. Profit on selling one mixer and one food processor is Rs 2,000 and Rs 3,000 respectively. Both the products are processed through three machines A, B, C. The time required in hours for each product and total time available in hours per week on each machine arc as follows:

How many mixers and food processors should be produced in order to maximize the profit?

Find the feasible solution of the following inequation:

3x + 4y ≥ 12, 4x + 7y ≤ 28, y ≥ 1, x ≥ 0.