Assume that the volume discounts in Table 1 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 79. Does one always produce a lower price than the other? Discuss.