A kids' organization sold 570 bars last year at $ 2.55 per candy bar. Research has suggested that for each $ 0.25 price increase, they will sell 20 less candy bars. They want to know what price should they sell their candy bars at to maximize their revenue. Please help them out, showing your work neatly in the following steps. And please label the steps clearly with the letters A through F A) Define your variables. This means that for every letter you use to represent a value, you communicate what it equals in words. B) Find the linear equation that relates the price and the number sold. C) Determine a function that represents the Revenue. (Remember, Revenue = (Price)*(Number Sold)).

Survey Of Economics
10th Edition
ISBN:9781337111522
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter1: Introducing The Economic Way Of Thinking
Section1.A: Applying Graphs To Economics
Problem 2SQP
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A kids' organization sold 570 bars last year at $ 2.55 per candy bar. Research has suggested that for each $
0.25 price increase, they will sell 20 less candy bars. They want to know what price should they sell their
candy bars at to maximize their revenue.
Please help them out, showing your work neatly in the following steps. And please label the steps clearly
with the letters A through F
A) Define your variables. This means that for every letter you use to represent a value, you communicate
what it equals in words.
B) Find the linear equation that relates the price and the number sold.
C) Determine a function that represents the Revenue.
(Remember, Revenue = (Price)*(Number Sold)).
D) Graph your revenue function on your calculator or Desmos or something similar and on your paper,
labeling the axes and the maximum point.
E) Uusing your calculator or Desmos or something similar, use your graph to determine the price that
maximizes the revenue for the organization.
Do NOT use calculus to solve this problem. (In other words, if you seek out help, don't let those that
help you show you how to do it with calculus. If they use the word "derivative," that's calculus.)
The price of a candy bar that maximizes the revenue is $
Round to the nearest cent.
F) Also, determine the number they will sell at this price:
The number of candy bars they will sell at that price is
Round to the nearest whole number.
Transcribed Image Text:A kids' organization sold 570 bars last year at $ 2.55 per candy bar. Research has suggested that for each $ 0.25 price increase, they will sell 20 less candy bars. They want to know what price should they sell their candy bars at to maximize their revenue. Please help them out, showing your work neatly in the following steps. And please label the steps clearly with the letters A through F A) Define your variables. This means that for every letter you use to represent a value, you communicate what it equals in words. B) Find the linear equation that relates the price and the number sold. C) Determine a function that represents the Revenue. (Remember, Revenue = (Price)*(Number Sold)). D) Graph your revenue function on your calculator or Desmos or something similar and on your paper, labeling the axes and the maximum point. E) Uusing your calculator or Desmos or something similar, use your graph to determine the price that maximizes the revenue for the organization. Do NOT use calculus to solve this problem. (In other words, if you seek out help, don't let those that help you show you how to do it with calculus. If they use the word "derivative," that's calculus.) The price of a candy bar that maximizes the revenue is $ Round to the nearest cent. F) Also, determine the number they will sell at this price: The number of candy bars they will sell at that price is Round to the nearest whole number.
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