NCERT Class 12-Mathematics: Chapter –12 Linear Programming Part 6

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Question 11:

A manufacturer of electronic circuits has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs 50 and that on type B circuit is Rs 60, formulate this problem as a LPP so that the manufacturer can maximise his profit.

Answer:

Maximise , subject to:

Question 12:

A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each. The cost for engaging each large van is Rs 400 and each small van is Rs 200. Not more than Rs 3000 is to be spent on the job and the number of large vans can-not exceed the number of small vans. Formulate this problem as a LPP given that the objective is to minimise cost.

Answer:

Minimise , subject to:

Question 13:

A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of Type A screws requires 2 minutes on the threading machine and 3 minutes on the slotting machine. A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine. In a week, each machine is available for 60 hours. On selling these screws, the company gets a profit of Rs 100 per box on type A screws and Rs 170 per box on type B screws.

Formulate this problem as a LPP given that the objective is to maximise profit.

Answer:

Maximise subject to constraints

Question 14:

A company manufactures two types of sweaters: type A and type B. It costs Rs 360 to make a type A sweater and Rs 120 to make a type B sweater. The company can make at most 300 sweaters and spend at most Rs 72000 a day. The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100. The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.

Formulate this problem as a LPP to maximise the profit to the company.

Answer:

Thus, the required LPP to maximise the profit is Maximise is subject to constraints.

Question 15:

A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has at-most Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel.

Express this problem as a linear programming problem.

Answer:

Maximise

Long Answer (L.A)

Question 16:

Refer to Exercise 11. How many of circuits of Type A and of Type B, should be produced by the manufacturer so as to maximise his profit? Determine the maximum profit.

Answer:

Type , Type ; Maximum

Question 17:

Refer to Exercise 12. What will be the minimum cost?

Answer:

The minimum cost is

Question 18:

Refer to Exercise 13. Solve the linear programming problem and determine the maximum profit to the manufacturer.

Answer:

The maximum profit to the manufacture is 138600.

Question 19:

Refer to Exercise 14. How many sweaters of each type should the company make in a day to get a maximum profit? What is the maximum profit.

Answer:

Question 20:

Refer to Exercise 15. Determine the maximum distance that the man can travel.

Answer:

The maximum distance that the man can travel is

Question 21:

Maximise subject to .

Answer:

The maximum value is

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