Question

2. A local t-shirt company sold 2000 t-shirts two weeks ago when they charged $10 for each shirt. The following week they sold 1120 t-shirts when they raised the price to $19 per shirt. Assuming that this rate of change continues find the following: a. Find a linear function S(p) that models the number of shirts sold as a function of the price p. b. Explain the meaning of the slope In terms of the problem. c. Predict the number of shirts the store would sell if they charged $25 for each shirt. d. If the store would like to maintain a weekly sales level of 1450 shirts how much should they charge per shirt?

Answer 1

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Answer:

a) S(p) = -97.78p +2977.78

b) about 98 fewer shirts per week will be sold for each $1 increase in price

c) 533 shirts per week

d) $15.63

Explanation:

a) You are given two ordered pairs: (p, s) = (10, 2000) and (19, 1120). The two-point form of the equation for a line can be used.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

s = (1120 -2000)/(19 -10)(p -10) +2000

s = -97.78(p -10) +2000

S(p) = -97.78p +2977.78

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b) The slope is shirts/dollar, meaning about 98 fewer shirts will be sold for each dollar increase in price.

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c) S(25) ≈ 533

At a price of $25, the store would sell about 533 shirts per week.

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d) 1450 = S(p) = -97.78p +2977.78

-1527.78 = -97.78p

15.625 = p ≈ 15.63

The store should charge $15.63 per shirt to maintain sales of 1450 shirts per week.