2. Previously you solved a problem in which the profits of a company in millions of dollars were modeled as a function of x, the number of franchises sold. The profits were modeled with the quadratic function: P = f(x) = -x² + 10x – 10. Algebraically find the vertex of this function and explain what it means about the profits of the company.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.2: Transformations Of Quadratic Functions
Problem 50PFA
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2. Previously you solved a problem in which the profits of a company in millions of dollars were
modeled as a function of x, the number of franchises sold. The profits were modeled with the
quadratic function: P = f(x) = -x² + 10x – 10. Algebraically find the vertex of this
function and explain what it means about the profits of the company.
3. You are the head of marketing at a large company. Your research has shown that the
company's annual profit, P in millions of dollars, is a function of the amount spent on
advertising, x, in thousands of dollars. You determine that you can model the annual profits
with the quadratic function: = 230 + 20x – 0.5x?. The CEO of the company is willing to
spend up to four hundred thousand dollars on advertising this year in order to achieve the
highest possible profits. What advice do you have for the CEO? This CEO always wants very
succinct advice, but he is also interested in the "whole picture". He insists on full
documentation in case he later wants to review the facts. Write a report that gives clear advice
for the CEO and fits the above specifications.
Transcribed Image Text:2. Previously you solved a problem in which the profits of a company in millions of dollars were modeled as a function of x, the number of franchises sold. The profits were modeled with the quadratic function: P = f(x) = -x² + 10x – 10. Algebraically find the vertex of this function and explain what it means about the profits of the company. 3. You are the head of marketing at a large company. Your research has shown that the company's annual profit, P in millions of dollars, is a function of the amount spent on advertising, x, in thousands of dollars. You determine that you can model the annual profits with the quadratic function: = 230 + 20x – 0.5x?. The CEO of the company is willing to spend up to four hundred thousand dollars on advertising this year in order to achieve the highest possible profits. What advice do you have for the CEO? This CEO always wants very succinct advice, but he is also interested in the "whole picture". He insists on full documentation in case he later wants to review the facts. Write a report that gives clear advice for the CEO and fits the above specifications.
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