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.
