R-So-100,Sooob-200-25-(-4) - 3009 1. A winery finds that it can sell 200 bottles
ID: 3147733 • Letter: R
Question
R-So-100,Sooob-200-25-(-4) - 3009 1. A winery finds that it can sell 200 bottles if it sells the wine for $25 per sell 100 bottles if it sets the price at $50 per bottle. Find the linear report the revenue function. At what price will the revenue be maximized? demand function. T What is the maximum If the winery in the previous problem finds that the cost for producing a boftle of wine is $1250 Report the linegr cost function (assume no fixed costs). Use the revenue and cost functions to build the proft funcfions. How much should the winery charge for each bottle if it wants to maximize the profit? What is the maximum profit? Cemo 2. 3. Due to the downturn in the economy, a stock that you purchased for $80 per share has been depreciating continuously at a rate of 4% per year for the last 3 years. What is the share price for the stock after the 3 years? Analysts predict that over the next two years, the stock price will grow continuously at a rate of 8% per year. If the stock prices grows as analysts predict, what will the stock price be in two years? What is the overall percent change over the five years? 4. Jessie sold 100 "I LOVE MATH" 1-shirts and sales appear to be doubling every 5 days. She estimates the total market for "I LOVE MATH t-shirts to be 4,000 units. Give a logistic model for Jessie's sales after t days and use it to predict, to the nearest day, when she will have sold 700 t-shirts. 5. In a period immediately following its initial public offering (IPO), a stock was doubling in value every 3 hours. If Nyoosha bought $10,000 worth of the stock when it was first offered, how much was her stock worth after 8 hours? The yearly lobster harvest from Long Island Sound has been decreasing dramatically since 1997, The size of the annual harvest can be approximated by nl-9.1081) million pounds where t is 6. time in year since 1997 a. The model tells us that the harvest wasmillion pounds in 1997 and decreasing by What does the model predict for the 2013 harvest? Round to two decimal places. The demand for Freon has been declining significantly in response to regulation and concern about % each year. b. 9· the ozone layer. The demand for Freon can be estimated as 71 fl)- +0.05(0.74) iounds in year t ( 0 corresponds to 1990) what is the demand for Freon in 2011? what was the demand for Freon in 1990? (Round to two decimal places)Explanation / Answer
y = demand x = price
(x,y) = (25,200) and (50,100)
slope = (200 - 100)/(25-50) = -2
hence
y = 250 -2x
or
D = 250 - 2p
revenue = R = p*D
= p*(250 - 2p)
it will be maximum when dR/dp = 0
= 250 - 4p
hence p = 62.5
hence
R max = 62.5 * (250 -2 *62.5) = 7812.5
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