Minimum cost Question?

Question

The cost
(in dollars) of manufacturing
radios at Christine's Stereo World is given by the function C(x)=0.1x^2-24x+16,452 What is the minimum cost of manufacturing radios?

Answer 1

The cost function for manufacturing radios is C(x)=0.1x²-24x+16,452 .

To find minimum cost , equate the first derivative of cost function to zero .

C'(x)=(0.1)2x - 24 =  0

0.2x - 24 =  0

0.2x = 24

x = 24 / 0.2

x = 120 .

To achieve  minimum cost for manufacturing , company have to manufacture 120 radios .

minimum cost =  C(120) = 0.1(120)² - 24(120) +16,452

C(120) = 1440 - 2880 +16,452

C(120) = 15012 .

So the minimum cost (in dollars) of manufacturing radios $15012 .