CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. Anil Kumar Tondak

CBSE CLASS XII

Linear Programming

Q. 1. One kind of cake requires 200gm of flour and 25gm of fat, and another kind of cake requires 100gm of flour and 50gm of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1kg of fat assuming that there is no shortage of the other ingredients used in  making the cakes.

Q. 2. 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 Rs. 16 and one Kg of food Y costs Rs. 20. Find the least cost of the mixture which will produce the required diet.

Q. 3. Maximise and Minimise:
Z = x + 2y
Subject to constraints   

Q. 4. An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit.

Q. 5. Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops are given in  following table :

Transportation Cost Per Quintal (in Rs.)

How should the supplies be transported in order that the transportation cost is minimum. What is the minimum cost.

Q. 6. Two tailors A and B earn Rs. 150 and Rs. 200 per day respectively. A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. Form a linear programming problem to minimize the labour cost to produce at least 60 shirts and 32 pants.

Q. 7. Solve the following L.P.P graphically:

Q. 8. A dealer wishes to purchase a number of fans and sewing machines. He has only Rs 5,760 to invest and has space for at most 20 items.  A fan costs him Rs. 360 and a sewing machine Rs 240. His expectation is that he can sell a fan at a profit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit.

Q. 9. If a young man drives his vehicle at 25 km/hr, he has to spend Rs. 2/km on petrol. If he drives it at a faster speed of 40km/hr, the petrol cost increases to Rs. 5/km. He has Rs. 100 to spend on petrol and travel within one hour. Express this as an L.P.P. and solve.

Q. 10. Determine graphically the minimum value of the objective function
Z = – 50x + 20y
subject to the constraints:

Q. 11. A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours ofcraftsman’s time.

1. What number of rackets and bats must be made if the factory is to work at full capacity?
2. If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.

Q. 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

Paper By Mr. Anil Kumar Tondak
Email Id : [email protected]