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

Last updated at Aug. 31, 2021 by Teachoo

An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves at least 20 seats for the executive class. However, at least 4 times as many passengers prefer to travel by economy class, than by executive class. It is given that the number of executive class tickets is x and that of economy class tickets is y.

Question An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves at least 20 seats for the executive class. However, at least 4 times as many passengers prefer to travel by economy class, than by executive class. It is given that the number of executive class tickets is x and that of economy class tickets is y.
Let the Number of Executive Class tickets = x
Number of Economy Class tickets = y
Given that
Aeroplane can carry a maximum of 200 passengers.
∴ x + y ≤ 200
Also, The airline reserves at least 20 seats for the executive class.
∴ x ≥ 20
And, at least 4 times as many passengers prefer to travel by economy class, than by executive class
y ≥ 4x
And, y ≥ 0
We would need to Maximize Profit
Given that
A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket
Z = 1000x + 600y
Combining all constraints :
Maximize Z = 1000x + 600y
Subject to Constraints :
x + y ≤ 200
y ≥ 4x
x ≥ 20
y ≥ 0
Question 1 The maximum value of x + y is_______. (a) 100 (b) 200 (c) 20 (d) 80
Since x + y ≤ 200
So, the correct answer is (B)
Question 2 The relation between x and y is_______. (a) x < y (b) y > 80 (c) x ≥ 4y (d) y ≥ 4x
From our constraints
y ≥ 4x
So, the correct answer is (D)
Question 3 Which among these is not a constraint for this LPP? (a) x ≥ 0 (b) x + y ≤ 200 (c) x ≥ 80 (d) 4x − y ≤ 0
Constraints for this Linear Programming Problem (LPP) are
x + y ≤ 200
y ≥ 4x
x ≥ 20
y ≥ 0
Since x ≥ 80 is not in the constraints
So, the correct answer is (C)
Question 4 The profit when x = 20 and y = 80 is _______. (a) Rs. 60000 (b) Rs. 68000 (c) Rs. 64000 (d) Rs. 136000
Now,
Z = 1000x + 600y
Putting x = 20, y = 80
Z = 1000(20) + 600(80)
Z = 20,000 + 48,000
Z = 68,000
∴ Profit = Rs 68,000
So, the correct answer is (B)
Question 5 The maximum profit is Rs. _______. (a) 136000 (b) 128000 (c) 68000 (d) 120000
Our LPP is
Maximize Z = 1000x + 600y
Subject to Constraints :
x + y ≤ 200
y ≥ 4x
x ≥ 20, y ≥ 0
Hence, Profit will be maximum, if
Tickets of executive class = 40
Tickets of economy class = 160
Maximum Profit = Rs 1,36,000
So, the correct answer is (a)

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.