# determine the maximum revenue for the given companies

Job opportunity surveys have consistently shown a high demand for those who can use mathematics to model complex processes and make informed predictions of the future.A student should be able to demonstrate his or her level of sophistication with respect to the key, in-demand skills of communication, quantitative literacy, and critical thinking.

# Assignment:Determine the maximum revenue for the given companies.

**Maximizing Revenue**

The marketing department at Gadgets Galore has found that when certain iPod’s are sold at a price of *p* dollars per unit, the revenue *R* (in dollars) as a function of the price *p* can be demonstrated by the function given in the graph below.

Use the above graph to answer the questions stated in Part I of the Response Sheet.

The Response Sheet was posted with this document.

# PART I: Maximizing Revenue (Quantitative Literacy)

*Interpretation*: Using complete sentences, explain the information represented by the graph.*Representation and Calculations*: Find the approximate revenue when the price of the item isâ€¦Place cursor on the line to type your response.*p*=$20*R*=__________________*p*=$40*R*=__________________*p*=$60*R*=__________________*p*=$80*R*=__________________*p*=$100*R*=__________________*p*=$120*R*=__________________

*Application and analysis*: Make a judgment and draw appropriate conclusions based on the quantitative analysis of the data represented in the given graph. (Hint: Does the data lead you to the maximum point on the graph? How does knowing this projected maximum point help this company?)**Write at least two or three sentences to explain your answer.***Assumptions*: When looking at the graph, what did you assume about the data shown to make your estimate of the maximum revenue and the needed price to charge to reach this maximum revenue?**Write at least two or three sentences to explain your answer.**

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# PART II: Maximizing Revenue (Communication and Critical Thinking – includes QL6)

# Instructions:

Write a 250 – 400 word essay (about 3 – 4 paragraphs) explaining how to solve the following problem:

The John Deere Company has found that the revenue from sales of heavy-duty tractors is a function of the unit price p that it charges.If the revenue R is *R(p) = ***â€“ ***0.5p ^{2} + 1900p *, what unit price p should be charged to maximize revenue?What is the maximum revenue? What recommendations would you give the John Deere Company?

Pretend you are explaining this to someone who has not taken a math class in several years. Be sure to include the following in your explanation:

- what the
*p*and*R*represent, - the actual value of the maximum revenue and the price needed to achieve this value, and
- recommendations you would give the John Deere Company (Hint: How can the data you calculated be used to benefit the company? For example, why shouldnâ€™t the company charge $2000 or more for each tractor?)

Use proper English and full sentences with ideas separated into paragraphs. Spelling and grammar count!

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