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

Last updated at May 29, 2023 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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