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

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