Volume discount. Assume that the volume discounts in Table apply only to that portion of the volume in each interval. That is, the discounted price for a $4,000 purchase would be computed as follows:
300 + 0.97(700) + 0.95(2,000) + 0.93(1,000) = 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 $1,000. As x approaches $3,000.
(C) Compare this discount method with the one in Problem.Does one always produce a lower price than the other? Discuss.
Table Volume Discount (excluding tax)
Volume ($x) | Discount Amount |
$300 ≤ x < $1,000 | 3% |
$1,000 ≤ x < $3,000 | 5% |
$3,000 ≤ x < $5,000 | 7% |
$5,000 ≤ x | 10% |
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