When a popular style of running shoe is priced at $80, Runner\'s Emporium sells

Question

When a popular style of running shoe is priced at $80, Runner's Emporium sells an average of 96 pairs per week. Based on comparative research, management believes that for each decrease of $2.50 in price, four additional pairs of shoes could be sold weekly. Let n denote the number of $2.50 decreases in price and let q denote the number of pairs of shoes sold. Write an equation that gives n in terms of q. Write a function R that gives the expected weekly revenue from sales of this particular style of shoe as a function of p, the price per pair(in dollars). Determine the selling price per pair that will result in maximum possible revenue, as well as the maximum possible revenue. Determine the lowest price (to the nearest cent) that will result in weekly revenue of at least $7000 from sales of the shoes.

Explanation / Answer

p =70

Hence when price equals 70, revenue is maximum

Price of shoe 80 Average 96 pairs New price 80-2.5 n q 96+4n 2) Revenue R Sales (80-2.5n)(96+4n) p =80-2.5n n = (80-p)/2.5 n= 32-0.4p So R = (80-80+0.4p)(96+128-1.6p) R= 0.4p(224-1.6p) 3) For max R, use derivative test R' = 224(0.4)-0.64(2p) R" = -0.128 <0 Set R' =0 and solve 224(0.4) = 1.28p

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