Question 2 - Case Based Questions (MCQ) - Chapter 12 Class 12 Linear Programming

Last updated at April 16, 2024 by Teachoo

A dealer in rural area wishes to purchase a number of sewing machines. He has only Rs. 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs. 360 and a manually operated sewing machine Rs. 240. He can sell an electronic sewing machine at a profit of Rs. 22 and a manually operated machine at a profit of Rs. 18. Assume that the electronic sewing machines he can sell is x and that of manually operated machines is y.

Question A dealer in rural area wishes to purchase a number of sewing machines. He has only Rs. 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs. 360 and a manually operated sewing machine Rs. 240. He can sell an electronic sewing machine at a profit of Rs. 22 and a manually operated machine at a profit of Rs. 18. Assume that the electronic sewing machines he can sell is x and that of manually operated machines is y.
Let the Number of Electronic Sewing Machines = x
Number of Manual Sewing Machines = y
Given that
He has space for at most 20 items for storage
∴ x + y ≤ 20
Also, An electronic sewing machine cost him Rs. 360 and a manually operated sewing machine Rs. 240. And, he has only Rs. 5,760 to invest
∴ Cost of electronic + Cost of manual ≤ 5760
Number of Electronic × 360 + Number of Manual × 240 ≤ 5760
360x + 240y ≤ 5760
Dividing both sides by 120
3x + 2y ≤ 48
Also,
x ≥ 0, y ≥ 0
We would need to Maximize Profit
He can sell an electronic sewing machine at a profit of Rs. 22 and a manually operated machine at a profit of Rs. 18
Z = 22x + 18y
Combining all constraints :
Maximize Z = 22x + 18y
Subject to Constraints :
x + y ≤ 20
3x + 2y ≤ 48
x ≥ 0, y ≥ 0
Question 1 The objective function is _______. (a) Maximise Z = 360x + 240y (b) Maximise Z = 22x + 18y (c) Minimise Z = 360x + 240y (d) Minimise Z = 22x + 18y
Objective function is
Maximize Z = 22x + 18y
So, the correct answer is (B)
Question 2 The maximum value of x + y is _______. (a) 5760 (b) 18 (c) 22 (d) 20
Since
x + y ≤ 20
Thus, Maximum value of x + y is 20
So, the correct answer is (D)
Question 3 Which of the following is not a constraint? (a) x + y ≥ 20 (b) 360x + 240y ≤ 5760 (c) x ≥ 0 (d) y ≥ 0
Our LPP is
Maximize Z = 22x + 18y
Subject to Constraints :
x + y ≤ 20
3x + 2y ≤ 48
x ≥ 0, y ≥ 0
Since x + y ≤ 20, not greater than
So, the correct answer is (A)
Question 4 The profit is maximum when (x, y) = _______. (a) (5, 15) (b) (8, 12) (c) (12, 8) (d) (15, 5)
Our LPP is
Maximize Z = 22x + 18y
Subject to Constraints :
x + y ≤ 20
3x + 2y ≤ 48
x ≥ 0, y ≥ 0
So, the correct answer is (B)
Question 4 The profit is maximum when (x, y) = _______. (a) (5, 15) (b) (8, 12) (c) (12, 8) (d) (15, 5)
Our LPP is
Maximize Z = 22x + 18y
Subject to Constraints :
x + y ≤ 20
3x + 2y ≤ 48
x ≥ 0, y ≥ 0
∴ Z = 392 is maximum at (8, 12)
So, the correct answer is (b)
Question 5 The maximum profit is Rs. _______. (a) 5760 (b) 392 (c) 362 (d) 290
Since Z = 392 is maximum at (8, 12)
∴ Maximum Profit = Rs 392
So, the correct answer is (B)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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