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A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?
  • a)
    3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.
  • b)
    4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.
  • c)
    3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.
  • d)
    4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A manufacturer produces nuts and bolts. It takes 1 hour of work on mac...
Let number of packages of nuts produced = x 
And number of packages of bolts produced = y 
Therefore , the above L.P.P. is given as : 
Maximise , Z = 17.50x +7y , subject to the constraints : x +3y ≤ 12 and. 3x +y ≤ 12, x, y ≥ 0.

i.e 3 packages of nuts and 3 packages of bolts;
Maximum profit = Rs 73.50.
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Most Upvoted Answer
A manufacturer produces nuts and bolts. It takes 1 hour of work on mac...
To maximize the profit, we need to determine the number of packages of nuts and bolts that should be produced each day, given the constraints of the machines' operating hours.

Let's assume that x packages of nuts and y packages of bolts are produced each day.

The time constraint can be represented by the following equation:
1x + 3y ≤ 12 (since machine A takes 1 hour for nuts and 3 hours for bolts, and the total operating hours is 12)

Next, we need to consider the profit constraint. The profit for nuts is Rs17.50 per package, and the profit for bolts is Rs7.00 per package.

The profit equation can be represented as:
Profit = 17.50x + 7.00y

To determine the maximum profit, we need to find the maximum value of the profit equation subject to the constraints mentioned above.

Solving the above equations graphically or using linear programming techniques, we find that the maximum profit is obtained when x = 3 and y = 3.

Substituting these values into the profit equation:
Profit = 17.50(3) + 7.00(3) = Rs 52.50 + Rs 21.00 = Rs 73.50

Therefore, the correct answer is option 'A': 3 packages of nuts and 3 packages of bolts, with a maximum profit of Rs 73.50.
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A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer?
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A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer?.
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Here you can find the meaning of A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?a)3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.b)4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.c)3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.d)4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
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