The total cost of producing x coffee machines is C(x)=2000+70x−0.1x2 A. Find the exact cost of producing the 21st machine B. Use marginal cost to approximate the cost of producing the 21st machine

Answer 1

The exact cost can be found by doing C(21)-C(20) so:

2000+70(21)-.1(21)²-(2000+70(20)-.1(20²)=$65.90

marginal cost can be found by taking the derivative of the function and then plugging in 20 (yes 20 because you want to find the additional cost after producing the 20th unit)

C'(x)=70-.2x

C'(20)=70-.2(20)=$66