Question

Suppose the cost function for the production of a new item is given by the equation

C(x) = 2x^2-320x + 12920, where x represents the number of items. How many items
should be produced to minimize the cost?

Answer 1

x=80

Explanation:

Take the derivative of C(x) using the power rule

C'(x)=4x-320

Set this equal to 0 and solve for x

4x=320

x=80.

Sign analysis shows this to be a minimum because for values larger than 80 C'(x)>0 and for values less than 80 C'(x)<0