integration sum application

Question

Marginal cost (MC) as a function of units of product x is given by:

MC=1.064-0.005x. Find the total and average cost function is fixed cost is 16.3

 

sum of application of integration in business.

please give detailed answer with proper statements.

thanks

 

Answer 1

Total cost = C(x) = ∫(1.064 - 0.005x)dx = 1.064x - 0.0025x² + K

 

    Since C(0) = 16.3, we get  K = 16.3

 

    So, C(x) = 1.064x - 0.0025x² + 16.3

 

Average cost = C(x)/x = 1.064 - 0.0025x + 16.3/x

 

Answer 2

Take the anti-derivative of MC to get average cost function, C(x).

 

C(x) = 1.064x - 0.0025x² + K

 

 

where K is an arbitrary constant.  Solve for K using the initial value condition    C(0)=16.3

 

 

Then your total cost is     MC + C(x)