Question 2 - Case Based Questions (MCQ) - Chapter 12 Class 12 Linear Programming (Term 1)

Last updated at Aug. 31, 2021 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)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.