Question

The function C(x)=300x+6,000 represents the cost to produce x number of items. How many items should be produced so that the average cost is less than $500?

Answer 1

Answer:

More than 30 items

Step-by-step explanation:

C(x)=300x+6,000

First, find c(x), the average cost function.

c(x)c(x)=C(x)x=300x+6,000x

The average cost function is shown below.

c(x)=300x+6,000x

We want the function c(x) to be less than 500.

c(x)<500

Substitute the rational expression for c(x).

300x+6,000x<500x≠0

Subtract 500 to get 0 on the right.

300x+,6000x−500<0

Find the LCD, and rewrite the left side as one quotient.

300x+6,000x−500xx−200x+6,000x<0<0

Factor the numerator to show all factors.

−200(x−30)x<0

Find the critical points when the numerator or denominator are equal to 0.

−200(x−30)−200≠0x−30x=0x=0=0=30

More than 30 items must be produced to keep the average cost below $500 per item.