JEE Exam > JEE Questions > One kind of cake requires 200g of flour and 2...
Start Learning for Free
One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.
- a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kind
- b)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kind
- c)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kind
- d)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kind
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
One kind of cake requires 200g of flour and 25g of fat, and another ki...
Let number of cakes of first type = x
And number of cakes of second type = y
Therefore , the above L.P.P. is given as :
Minimise , Z = x +y , subject to the constraints : 200x +100y ≤ 5000 and. 25x +50y ≤ 1000, i.e. 2x + y ≤ 50 and x +2y ≤ 40 x, y ≥ 0.
i.e Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kind .
And number of cakes of second type = y
Therefore , the above L.P.P. is given as :
Minimise , Z = x +y , subject to the constraints : 200x +100y ≤ 5000 and. 25x +50y ≤ 1000, i.e. 2x + y ≤ 50 and x +2y ≤ 40 x, y ≥ 0.
i.e Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kind .
Most Upvoted Answer
One kind of cake requires 200g of flour and 25g of fat, and another ki...
Solution:
Given, One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat.
Let x be the number of cakes of the first kind and y be the number of cakes of the second kind.
So, the total amount of flour required = 200x + 100y grams.
The total amount of fat required = 25x + 50y grams.
Now, we have 5kg of flour and 1kg of fat.
1 kg = 1000g
∴ 5kg of flour = 5000g of flour
and 1kg of fat = 1000g of fat.
Therefore, we have the following equations:
200x + 100y ≤ 5000 … (1)
25x + 50y ≤ 1000 … (2)
We need to maximize x + y subject to the above constraints.
Let us plot the lines corresponding to the above two equations.
The line corresponding to equation (1) is 2x + y = 50 and the line corresponding to equation (2) is x + 2y = 20.
The feasible region is the shaded region in the figure below.
The vertices of the feasible region are (0, 20), (5, 0), and (10, 0).
Now, we need to find the maximum value of x + y subject to the above constraints.
At the vertex (5, 0), we have x + y = 5.
At the vertex (0, 20), we have x + y = 20.
At the vertex (10, 0), we have x + y = 10.
Therefore, the maximum value of x + y is 20, which occurs at the vertex (0, 20).
Hence, the maximum number of cakes that can be made is 20 of the first kind and 10 of the second kind, i.e., a total of 30 cakes.
Therefore, option (A) is the correct answer.
Given, One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat.
Let x be the number of cakes of the first kind and y be the number of cakes of the second kind.
So, the total amount of flour required = 200x + 100y grams.
The total amount of fat required = 25x + 50y grams.
Now, we have 5kg of flour and 1kg of fat.
1 kg = 1000g
∴ 5kg of flour = 5000g of flour
and 1kg of fat = 1000g of fat.
Therefore, we have the following equations:
200x + 100y ≤ 5000 … (1)
25x + 50y ≤ 1000 … (2)
We need to maximize x + y subject to the above constraints.
Let us plot the lines corresponding to the above two equations.
The line corresponding to equation (1) is 2x + y = 50 and the line corresponding to equation (2) is x + 2y = 20.
The feasible region is the shaded region in the figure below.
The vertices of the feasible region are (0, 20), (5, 0), and (10, 0).
Now, we need to find the maximum value of x + y subject to the above constraints.
At the vertex (5, 0), we have x + y = 5.
At the vertex (0, 20), we have x + y = 20.
At the vertex (10, 0), we have x + y = 10.
Therefore, the maximum value of x + y is 20, which occurs at the vertex (0, 20).
Hence, the maximum number of cakes that can be made is 20 of the first kind and 10 of the second kind, i.e., a total of 30 cakes.
Therefore, option (A) is the correct answer.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer?
Question Description
One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect 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 One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect 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 One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer?.
One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect 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 One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect 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 One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer?.
Solutions for One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.a)Maximum number of cakes = 30 , 20 of kind one and 10 cakes of another kindb)Maximum number of cakes = 32 , 20 of kind one and 12 cakes of another kindc)Maximum number of cakes = 34 , 27 of kind one and 7 cakes of another kindd)Maximum number of cakes = 33 , 22 of kind one and 11 cakes of another kindCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup