Question

A book company determines that the marginal costs of the xth book is given by:
C’(x) = -0.0002x + 1.25, and C(0) = $100. Find the total cost of producing 5,000 cookie

Answer 1

integrate c'(x)
we get c(x)=-0.0002x^2/2+1.25x+k
now for x=0 we have c(x)=100
puttin x =0 we get c(0)=k
so k=100
so
cost function c(x)=-0.0001x^2+1.25x+100
total cost of producing 5000 books
c(5000)=-0.0001*5000^2+1.25*5000+100
=-2500+6250+100
=$3850

Answer 2

thnx