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.
Answer:
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:
Tablets | Iron | Calcium | Vitamin |
X | |||
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?
Answer:
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.
Answer:
Question 25:
Maximise and Minimise subject to
Answer:
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
Column A | Column B |
Maximum of Z | 325 |
(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
(A)
(B)
(C)
(D)
Answer: B
Question 28:
Refer to Exercise 27. Maximum of Z occurs at
(A)
(B)
(C)
(D)
Answer: A