The total cost C(x) associated with the production of x units of an item is given by $C(x) = 0.001x^3 +0.06x^2 + 20x + 500$. The marginal cost when 10 units are produced is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 21.5
Given total cost:
$C(x)=0.001x^{3}+0.06x^{2}+20x+500$
Marginal cost = derivative of $C(x)$:
$C'(x)=0.003x^{2}+0.12x+20$
At $x = 10$:
$C'(10)=0.003(100)+0.12(10)+20$
$=0.3 + 1.2 + 20$
$=21.5$
The marginal cost when 10 units are produced is 21.5.