The cost, in thousands of dollars, of airing x television commercials during a s

Question

The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2, 500x - 0.06x^2. (a) Find the marginal cost function C'(x). C'(x) = Use it to determine how fast the cost is increasing when x = 4. thousand dollars 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 dollars What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.

Explanation / Answer

C(x) = 150 + 2500x - 0.06x^2

a) C'(x) = 2500 - 0.12x

When x = 4

C'(x) = 2500 - 0.12*4 = 2499.52

When x = 5

C'(5) = 2500 - 0.12*5 = 2499.40

The cost is going up at the rate of 2499.52 - 2499.40 = 0.12$

The exact cost of airing the fifth commercial is $2,250,000
the cost of 5 commercials is $12648.5 * 1000 as it is in thousands of dollars ( plug 5 into C(x))
You would need to compare to C(4)= 10149.04*1000
.Thus, there is a difference of $ 2499460

b) Divide by x to find average cost function

C(x) = 150/x + 2500 - 0.06x
_
C(4) = $2537.26( thousands) = $2,537,260

if you buy four commercials, they average $2,537,260 each.
The average cost of airing the first four commercials is $2,537,260 each
or 4(2,537,260)= $ 10149,040 for all four.

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