Question

A small company manufactures custom-designed mugs. The total cost (in ₹) of producing x mugs is given by C(x)=0.1x³-3x²+50x+200

What is the marginal cost when 20 mugs are produced?

• A. ₹ 80
• B. ₹ 50
• C. ₹ 55
• D. ₹ 800

Answer 1

Answer: (B)

₹ 50

Answer 2

The total cost function is given by $C(x) = 0.1x^3 - 3x^2 + 50x + 200$.

Marginal cost (MC) is the derivative of the total cost function with respect to the number of mugs produced, $x$.

$MC = \frac{dC}{dx}$

Differentiating $C(x)$ with respect to $x$:

$MC = \frac{d}{dx}(0.1x^3 - 3x^2 + 50x + 200)$

$MC = 0.1(3x^2) - 3(2x) + 50(1) + 0$

$MC = 0.3x^2 - 6x + 50$

To find the marginal cost when 20 mugs are produced, substitute $x = 20$ into the marginal cost function:

$MC(20) = 0.3(20)^2 - 6(20) + 50$

$MC(20) = 0.3(400) - 120 + 50$

$MC(20) = 120 - 120 + 50$

$MC(20) = 50$

Therefore, the marginal cost when 20 mugs are produced is ₹ 50.