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GATE | GATE CS 2012 | Question 56

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  • Difficulty Level : Medium
  • Last Updated : 17 May, 2019
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The cost function for a product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of Rs 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
(A) 5
(B) 10
(C) 15
(D) 25

Answer: (A)


Profit = Price - Cost
       = 50q - 5q2
The above function will be maximum for the values on which its first derivative becomes 0.
        50 - 10*q = 0
        50 = 10 * q
        q = 5.
The value of above expression is maximum at q = 5. 

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