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.

This question is inspired from Misc 5 - Chapter 12 Class 12 (Linear Programming)

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Question 1

The maximum value of x + y is_______.

(a) 100  

(b) 200

(c) 20  

(d) 80

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Question 2

The relation between x and y is_______.

(a) x < y 

(b) y > 80

(c) x ≥ 4y      

(d) y ≥ 4x

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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

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Question 4

The profit when x = 20 and y = 80 is  _______.

(a) Rs. 60000  

(b) Rs. 68000

(c) Rs. 64000  

(d) Rs. 136000

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Question 5

The maximum profit is Rs.  _______.

(a) 136000 

(b) 128000

(c) 68000 

(d) 120000 

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Transcript

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)

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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.