Find the marginal cost when 800 units are produced

Question

Suppose that the total cost in dollars of producing x units of a product is given by

C(x) = 5,000 + 30xe^x/800.

Find the marginal cost when 800 units are produced

Answer 1

Suppose that the total cost in dollars of producing x units of a product is given by

C(x) = 5,000 + 30xe^x/800.

Find the marginal cost when 800 units are produced

SOLUTION

The marginal cost when 800 units are produced is equal

to C' (800)

C'(x) = 30e^x/800. + 30xe^x/800.( 1/ 800 )

Then C'(800) =$ 163.096 which is of course an approximation.

The actual cost for producing the 801st unit is C (801) -C( 800 ) =$70402.01 - $70238.76 = $163.25

The derivative as you see did a pretty good job