How many bookcases should the company produce each month in order to achieve an average cost of $150? (Round your answer to the nearest whole bookcase.)

Question

A company produces bookcases. The average cost to produce x bookcases can be modeled by the function

c(x)= 7856+80x / x

Answer 1

c(x) = (7856 + 80x)/x

average cost = total cost divided by quantity

c(x)/x =150 = (7856+8x)/x^2

150x^2 = 8x + 7856

150x^2 -8x - 7856 = 0

x= 8/300 + or - (1/300)sqr(64+600(7856) = 7 book cases, rounded off to nearest whole number

ignore the negative solution

Alternatively, if you did intend c(x)=150= average cost, then

c(x)=150 = (7856+8x)/x

150x =7856+8x

142x = 7856

x = 7856/142 = 55 book cases, rounded off to nearest whole number

that's probably the answer you want.

but c(x) is usually used for total cost, with AC= average cost = c(x)/x for per unit cost

so, go with 55