NCERT Class 12-Mathematics: Chapter –12 Linear Programming Part 7

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Question 22:

A manufacturer produces two Models of bikes - Model X and Model Y. Model X takes a 6 man-hours to make per unit, while Model Y takes 10 man-hours per unit. There is a total of 450 man-hour available per week. Handling and Marketing costs are Rs 2000 and Rs 1000 per unit for Models X and Y respectively. The total funds available for these purposes are Rs 80,000 per week. Profits per unit for Models X and Y are Rs 1000 and Rs 500, respectively.

How many bikes of each model should the manufacturer produce so as to yield a maximum profit? Find the maximum profit.


Question 23:

In order to supplement daily diet, a person wishes to take some X and some wishes Y tablets. The contents of iron, calcium and vitamins in X and Y (in milligrams per tablet) are given as below:

The contents of iron, calcium and vitamins in X and Y







The person needs at least 18 milligrams of iron, 21 milligrams of calcium and 16 milligram of vitamins. The price of each tablet of X and Y is Rs 2 and Re 1 respectively. How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost?


Question 24:

A company makes 3 model of calculators: A, B and C at factory I and factory II. The company has orders for at least 6400 calculators of model A, 4000 calculator of model B and 4800 calculator of model C. At factory I, 50 calculators of model A, 50 of model B and 30 of model C are made every day; at factory II, 40 calculators of model A, 20 of model B and 40 of model C are made every day. It costs Rs 12000 and Rs 15000 each day to operate factory I and II, respectively. Find the number of days each factory should operate to minimise the operating costs and still meet the demand.


Question 25:

Maximise and Minimise subject to


Objective Type Questions

Choose the Correct Answer from the Given Four Options in Each of the Exercises 26 to 34

Question 26:

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y.

Compare the quantity in Column A and Column B

Compare the quantity in Column A and Column B

Column A

Column B

Maximum of Z


(A) The quantity in column A is greater

(B) The quantity in column B is greater

(C) The two quantities are equal

(D) The relationship can-not be determined on the basis of the information supplied

Answer: B

Question 27:

The feasible solution for a LPP is shown in Fig. 12.12. Let be the objective function. Minimum of Z occurs at

Fig.12.12-The feasible solution for a LPP

The Feasible Solution for a LPP

Loading image





Answer: B

Question 28:

Refer to Exercise 27. Maximum of Z occurs at





Answer: A