Question

Compare this with the exact cost of airing the fifth commercial.The cost is going up at the rate of $_______ per television commercial. The exact cost of airing the fifth commercial is $_____ . Thus, there is a difference of $_______ .(b) Find the average cost function C, and evaluate C(4).C(x) =__________ C(4) =_________ thousand dollarsWhat does the answer tell you?The average cost of airing the first four commercials is $_______ per commercial.

Answer 1

Answer:

a) Marginal cost = 2400 - 0.08x

At x = 4, marginal cost = $2399.68 thousand dollars

The cost is going up at the rate of **$ (2400 - 0.08 (x))** per television commercial. The exact cost of airing the fifth commercial is **$2399.64 thousand dollars**. Thus, there is a difference of **$0.04 thousand dollars**.

b) Average cost function = (150/x) + 2400 - 0.04x

At x = 4, C(4) = 2,437.34

The average cost of airing the first four commercials is **$2437.34 thousand dollars** per commercial.

Step-by-step explanation:

C(x) = 150 + 2400x − 0.04x²

Marginal cost = C'(x) = dC/dx = 2400 - 0.08x

At x = 4,

C'(x) = 2400 - 0.08(4) = 2399.68

The rate of increase is obviously [2400 - 0.08(x)]

The exact cost of airing the 5th commercial

C(5) - C(4)

= [150 + 2400(5) - 0.04(5²)] - [150 + 2400(4) - 0.04(4²) = 12149 - 9749.36 = $ 2399.64 thousand dollars

C'(5) = 2400 - 0.08(5) = 2399.6 thousand dollars.

b) Average cost = Total cost/quantity = [C(x)]/x= (150 + 2400x − 0.04x²)/x = (150/x) + 2400 - 0.04x

At x = 4, C(4) =

Average cost function = (150/4) + 2400 - 0.04(4) = $2,437.34 thousand dollars.