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A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?
- a)5 tennis rackets and 15 cricket bats
- b)4 tennis rackets and 12 cricket bats
- c)4 tennis rackets and 14 cricket bats
- d)3 tennis rackets and 13 cricket bats
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A factory makes tennis rackets and cricket bats. A tennis racket takes...
Let number of rackets made = x
And number of bats made = y
Therefore , the above L.P.P. is given as :
Maximise , Z = x +y , subject to the constraints : 1.5x +3y ≤ 42 and. 3x +y ≤ 24, i.e.0.5x + y ≤ 14 i.e. x +2y ≤ 28 and 3x +y ≤ 24 , x, y ≥ 0.
Here Z = 16 is maximum. i.e Maximum number of rackets = 4 and number of bats = 12.
And number of bats made = y
Therefore , the above L.P.P. is given as :
Maximise , Z = x +y , subject to the constraints : 1.5x +3y ≤ 42 and. 3x +y ≤ 24, i.e.0.5x + y ≤ 14 i.e. x +2y ≤ 28 and 3x +y ≤ 24 , x, y ≥ 0.
Here Z = 16 is maximum. i.e Maximum number of rackets = 4 and number of bats = 12.
Most Upvoted Answer
A factory makes tennis rackets and cricket bats. A tennis racket takes...
To determine the number of tennis rackets and cricket bats that must be made in order for the factory to work at full capacity, we need to consider the available machine time and craftsmans time.
Given:
- Tennis racket: 1.5 hours of machine time and 3 hours of craftsmans time
- Cricket bat: 3 hours of machine time and 1 hour of craftsmans time
- Maximum available machine time: 42 hours
- Maximum available craftsmans time: 24 hours
Let's solve this problem step by step.
1. Determine the maximum number of tennis rackets that can be produced:
- Since 1 tennis racket requires 1.5 hours of machine time, the maximum number of tennis rackets that can be produced in terms of machine time is 42/1.5 = 28.
- However, each tennis racket also requires 3 hours of craftsmans time. So, the maximum number of tennis rackets that can be produced in terms of craftsmans time is 24/3 = 8.
- The factory can only produce the number of tennis rackets that satisfies both conditions, which is the smaller value between 28 and 8. Therefore, the maximum number of tennis rackets that can be produced is 8.
2. Determine the maximum number of cricket bats that can be produced:
- Since 1 cricket bat requires 3 hours of machine time, the maximum number of cricket bats that can be produced in terms of machine time is 42/3 = 14.
- However, each cricket bat also requires 1 hour of craftsmans time. So, the maximum number of cricket bats that can be produced in terms of craftsmans time is 24/1 = 24.
- The factory can only produce the number of cricket bats that satisfies both conditions, which is the smaller value between 14 and 24. Therefore, the maximum number of cricket bats that can be produced is 14.
3. Determine the number of tennis rackets and cricket bats that must be made:
- Since the factory can only produce 8 tennis rackets and 14 cricket bats, the factory must make 8 tennis rackets and 14 cricket bats in order to work at full capacity.
Therefore, the correct answer is option 'B': 4 tennis rackets and 12 cricket bats.
Given:
- Tennis racket: 1.5 hours of machine time and 3 hours of craftsmans time
- Cricket bat: 3 hours of machine time and 1 hour of craftsmans time
- Maximum available machine time: 42 hours
- Maximum available craftsmans time: 24 hours
Let's solve this problem step by step.
1. Determine the maximum number of tennis rackets that can be produced:
- Since 1 tennis racket requires 1.5 hours of machine time, the maximum number of tennis rackets that can be produced in terms of machine time is 42/1.5 = 28.
- However, each tennis racket also requires 3 hours of craftsmans time. So, the maximum number of tennis rackets that can be produced in terms of craftsmans time is 24/3 = 8.
- The factory can only produce the number of tennis rackets that satisfies both conditions, which is the smaller value between 28 and 8. Therefore, the maximum number of tennis rackets that can be produced is 8.
2. Determine the maximum number of cricket bats that can be produced:
- Since 1 cricket bat requires 3 hours of machine time, the maximum number of cricket bats that can be produced in terms of machine time is 42/3 = 14.
- However, each cricket bat also requires 1 hour of craftsmans time. So, the maximum number of cricket bats that can be produced in terms of craftsmans time is 24/1 = 24.
- The factory can only produce the number of cricket bats that satisfies both conditions, which is the smaller value between 14 and 24. Therefore, the maximum number of cricket bats that can be produced is 14.
3. Determine the number of tennis rackets and cricket bats that must be made:
- Since the factory can only produce 8 tennis rackets and 14 cricket bats, the factory must make 8 tennis rackets and 14 cricket bats in order to work at full capacity.
Therefore, the correct answer is option 'B': 4 tennis rackets and 12 cricket bats.
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A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer?
Question Description
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer?.
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?a)5 tennis rackets and 15 cricket batsb)4 tennis rackets and 12 cricket batsc)4 tennis rackets and 14 cricket batsd)3 tennis rackets and 13 cricket batsCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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