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The cost function for a product in a firm is given by $5q^{2}$, where $q$ is the amount of production. The firm can sell the product at a market price of $\text₹ 50$ per unit. The number of units to be produced by the firm such that the profit is maximized is

  1. $5$
  2. $10$
  3. $15$
  4. $25$

2 Answers

Best answer
38 votes
38 votes

Answer is A.

The equation for profit is Profit $=SP-CP,$

Here, $SP=Q\times 50$  and $CP=5Q^{2}$.

So, when a function attains its maximum value its first order differentiation is zero.

Hence, $50-5\times 2\times Q=0 \therefore Q=5.$


For example :

5 units =  $CP = 125 \ SP=250 \ \therefore \text{Profit} =125$

10 units =  $CP = 500\ SP=500\therefore \;\text{Profit} =0$ and so forth..


Therefore, its maximum is at unit $= 5$

edited by
8 votes
8 votes

let x is the number of unit at which profit is maximized......

Profit(x):- Selling price(50*x) -production cost( 5x2 ) 

P(x)=50x-5x2   ...here we have to maximize the profit ..differentiate it..

d(P(x))/dx =50-10x =0  ...

x=5     ...option A

Answer:

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