Calculus Homework

Question

Suppose the cost of producing x widgets is C(x)=5000+40x−0.02x^2

A. What is the cost of producing widget number 31? Your answer should be a single number.

(Recall that C(x) is the cost of producing numbers 1,2,3,…up to x).

B. What is the marginal cost when x=30?

Answer 1

A. The cost of producing widget number 31 should be the cost of producing 31 widgets minus the cost of producing 30 widgets which is:

 

C(31) - C(30) = (5000 + 40*31 - 0.02*31²) - (5000 + 40*30 - 0.02*30²) = 6220.78 - 6182 = 38.78

 

B. Marginal Cost is defined as C'(x) since the cost equation is C(x).

 

C'(x) = 40 - 0.04x

 

C'(30) = 40 - 0.04*30 = 40 - 1.20 = 38.80