Answer to Question #270257 in Calculus for mimi

Question

if the total cost of producing x liters of salad oil is C(x)=0.375x^3-0.99x^2-200x+60,000

find the marginal cost at an output of 100litres

Answer 1

Solution;

Marginal coast is change in price that comes with producing an additional unit .

Hence:

$MC=C'(x)$

Given;

$C(x)=0.375x^3-0.99x^2-200x+60000$

Differentiate to get the marginal cost ;

$MC=C'(x)=1.125x^2-1.98x+200$

$x=100$

Hence by direct substitution;

$MC=1.125(100^2)-1.98(100)+200$

$MC=11,252$