Question

8) A company sells embroidered apparel. The volume discounts offered by the company are shown below, where x is the volume of a purchase in dollars.

Volume ($x)	Discount Amount
$300 ≤ x < $1000	3%
$1000 ≤ x < $3000	5%
$3000 ≤ x < $5000	7%
$5000 ≤ x	10%

Assume the volume discounts in Table 1 apply only to that portion of the volume in each interval. That is, the discounted price for a $4000 purchase would be computed as follows:

300 + .97(700) + .95(2000) +.93(1000) = 3,809

a. If x is the volume of a purchase before the discount is applied, then write a piecewise definition for the discounted price P(x) of this purchase.

b. Use one sided limits to investigate the limit of P(x) as x approaches $1000. What about as x approaches $3000?

Answer 1