An e-reader manufacturer expects to sel 60,000 units each year if the selling pr

Question

An e-reader manufacturer expects to sel 60,000 units each year if the selling price is $240. If the selling price is reduced to $180, then the manufacturer expects to sel 140,000 units each year a. Assume that the relationship between selling price ($) and units sold (1000s) is linear. Find the equation of the line that desorbes this relationship. Wrile your answer in slope-intercept form. Let x represent the seling price and y represent the units sold (1000s) b. Use your equation from part (a) to estimate the number of units thait the manufacturer expects to sell # the selling price is $150 Use the approximate values for the slope and y-intercept found in part a a. The egation, is use integers or decimaistr any runters n te equation Round the firal answer to two door al places as needed Round all rermodate valve to hrodeanal places·reeded ) b.The selling proe is $150, torne "antaare expects to sellunits. Use te appro mate values frthe siope and ynercept turd n per a Round to the nearest thousand as needed)

Explanation / Answer

a.Let x represent the selling price and y represent the units sold. The relation between x and y being linear, let us assume that y = mx+c, where m is the slope of the line and c is the y-intercept. Now, when x = 240, we have y = 60000 so that 60000 = 240m +c…(1). Similarly, 140000 = 180m +c..(2)On subtracting the 2nd equation from the 1st equation, we get 240m +c -180m –c = 60000-140000 or, 60m =-80000. Hence m = -80000/60 = -4000/3. Now, on substituting m = -4000/3 in the 1st equation, we get 240*(-4000/3)+c = 60000 or,c=60000+320000 or, c = 380000. Hence, the equation is y = (-4000/3)x+380000.

(b). When x = 150, then y = (-4000/3)*150 +380000 = -200000 +380000 = 180000. Thus, the manufacturer expects to sell 180000 units when the selling price is $ 150.

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