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The profit function p(x) of a firm , selling x items per day is given by p(x) = (150-x) x-1625. find the number of items the firm should manufacture to get maximum profit . find the maximum profit.
Answers
Given : The profit function p(x) of a firm , selling x items per day is given by p(x) = (150-x) x-1625
To find : number of items the firm should manufacture to get maximum profit .and the maximum profit.
Solution:
Profit function
P(x) = (150 - x) x - 1625
=> p(x) = 150x - x² - 1625
d(P(x))/dx = 150 - 2x
=> 150 - 2x = 0
=> x = 75
d²P(x)/dx² = - 2
Hence profit is Maximum when x = 75
Firm should manufacture 75 items to get maximum profit
Maximum Profit = (150 - 75)75 - 1625
= 5625 - 1625
= 4000
Firm should manufacture 75 items to get maximum profit
4000 is the Maximum profit
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