Question

The cost function for a product in a firm is
$givenby{\frac{5}{q}}^2,$
where q is the amount of production. The firm can sell the product at a market price of ₹ 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 1

The correct option is A 5

$TotalCostC=5q^2$

$TotalSalesRevenue,S=50q$

$Profit\left(P\right)=(S-C)=50q-5q^2$

As the profit have to be maximized

$P=50q-5q^2$

Using options:

(a) q = 5
P = 50 $\times$ 5 - 5 $\times 5^2$ = 125

(b) q = 10
P = 50 $\times$ 10 - 5 $\times {10}^2$ = 0

(c) q = 15
P = 50 $\times$15 - 5 $\times {15}^2$ = -ive

(d) q = 25
P = 50 $\times$ 25 - 5 $\times {25}^2$ = -ive

$Hencemaximumprofitwillhappenatq=5$

Alternative solution:

$P=50q-5q^2$

$Formax/min\frac{dp}{dq}=0$

$\Rightarrow 50-10q=0$
$q=10$

$\frac{d^{2}p}{d{Q}^2}{]}_{q=5}=-10whichisnegative$

$Hencemaximumprofitwillhappenatq=5$