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A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit is
Important : you should answer only the numeric value
Correct answer is '216'. Can you explain this answer?
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A plant manufactures compressors at the rate of N units/day. The daily...
Daily profit = selling price – cost price
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A plant manufactures compressors at the rate of N units/day. The daily...
Solution:
Given data:
Fixed charges = Rs. 20000
Variable cost per compressor = Rs. 500 + 0.2N^1.3
Selling price per compressor = Rs. 1000
The profit can be calculated as follows:
Profit = (Selling price - Variable cost) x Number of compressors manufactured - Fixed charges
P = (1000 - (500 + 0.2N^1.3)) x N - 20000
P = (500 - 0.2N^1.3) x N - 20000
To maximize the profit, we need to find the value of N at which the derivative of P with respect to N is zero.
dP/dN = 500 - 0.4N^1.3 - 0.2N^2.3 = 0
500 - 0.4N^1.3 - 0.2N^2.3 = 0
0.2N^2.3 + 0.4N^1.3 - 500 = 0
Using numerical methods or a graphing calculator, we can find that the solution to this equation is N = 216. Therefore, the number of compressors to be manufactured to maximize the daily profit is 216.
Answer: 216.
Given data:
Fixed charges = Rs. 20000
Variable cost per compressor = Rs. 500 + 0.2N^1.3
Selling price per compressor = Rs. 1000
The profit can be calculated as follows:
Profit = (Selling price - Variable cost) x Number of compressors manufactured - Fixed charges
P = (1000 - (500 + 0.2N^1.3)) x N - 20000
P = (500 - 0.2N^1.3) x N - 20000
To maximize the profit, we need to find the value of N at which the derivative of P with respect to N is zero.
dP/dN = 500 - 0.4N^1.3 - 0.2N^2.3 = 0
500 - 0.4N^1.3 - 0.2N^2.3 = 0
0.2N^2.3 + 0.4N^1.3 - 500 = 0
Using numerical methods or a graphing calculator, we can find that the solution to this equation is N = 216. Therefore, the number of compressors to be manufactured to maximize the daily profit is 216.
Answer: 216.
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A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit isImportant : you should answer only the numeric valueCorrect answer is '216'. Can you explain this answer?
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A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit isImportant : you should answer only the numeric valueCorrect answer is '216'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit isImportant : you should answer only the numeric valueCorrect answer is '216'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit isImportant : you should answer only the numeric valueCorrect answer is '216'. Can you explain this answer?.
A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit isImportant : you should answer only the numeric valueCorrect answer is '216'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit isImportant : you should answer only the numeric valueCorrect answer is '216'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit isImportant : you should answer only the numeric valueCorrect answer is '216'. Can you explain this answer?.
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