1.
Maximise Z = 3x + 4y Subject to the constraints: x + y < 4, x > 0, y > 0
Find the maximum value of Z?
2.
Maximise Z = 3x + 2y from the following graph:
3.
Minimise Z = −3x + 4y Subject to: x +2y < 8, 3x + 2y < 12, x > 0, y > 0
A.
Minimum value of Z is âˆ’10
B.
Minimum value of Z is âˆ’2
C.
Minimum value of Z is âˆ’15
D.
Minimum value of Z is âˆ’12
4.
Minimise and Maximise Z = x + 2y Subject to: x + 2y ≥ 100, 2x − y ≤ 0, 2x + y ≤ 200, x ≥ 0, y ≥ 0.
A.
Maximum value of Z is 400
B.
Minimum value of Z is 100
C.
D.
5.
Minimise Z = 3x + 5y Such that: x + 3y > 3, x + y > 2, x, y > 0
6.
Which of the following statements is true about an L.P. problem?
A. L.P.P. is concerned with finding the objective function of several variables subject to linear constraints
B. It refers to the method of determining a particular programme or plan of action.
C. The problem should have an optimal region inorder to have an optimal solution.
7.
In an L.P., the allowed numbers of constraints are:
8.
A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit.
A.
20 packages of screws A and 20 packages of screws B
B.
30 packages of screws A and 30 packages of screws B
C.
30 packages of screws A and 20 packages of screws B
D.
50 packages of screws A and 20 packages of screws B
9.
Minimise Z = 3x + 2y; subject to the constraints:
x + y ≥ 8
3x + 5y ≤ 15
x ≥ 0, y ≥ 0
10.
A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of grinding/cutting machine and a sprayer. It takes 2 hours on the grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes one hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is 5 and that from a shade is 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit? Make an L.P.P. and solve it graphically.
11.
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit, of Rs 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximize his profit, if he operates his machines for at the most 12 hours a day?
A.
3 packages of nuts and 6 packages of bolts
B.
3 packages of nuts and 3 packages of bolts
C.
6 packages of nuts and 3 packages of bolts
D.
3 packages of nuts and 8 packages of bolts
12.
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.
A.
Maximum value of Z is at (200, 50)
B.
Maximum value of Z is at (100, 50)
C.
Maximum value of Z is at (200, 100)
D.
Maximum value of Z is at (200, 150)
13.
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 4 hours of 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?
A.
Maximum value of Z is 500
B.
Maximum value of Z is 200
C.
Maximum value of Z is 400
D.
Maximum value of Z is 600
14.
There are two types of fertilizers F_{1} and F_{2}. F_{1} consists of 10% nitrogen and 6% phosphoric acid and F_{2} consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F_{1} cost Rs 6/kg and F_{2} costs Rs 5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
15.
A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F_{1}and F_{2} are available. Food F_{1} costs Rs 4 per unit food and F_{2} costs Rs 6 per unit. One unit of food F_{1 }contains 3 units of vitamin A and 4 units of minerals. One unit of food F_{2} 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?