2. A cereal company finds that the number of people who will buy one of its products in the first monththat it is introduced is linearly related. If it spends $40,000, on advertising, then 100,000 boxes of cerealwill be sold. And if it spends $60,000, then 200,000 boxes will be sold.a. Using the information provided, provide a linear model that describes the company's advertisingscheme. Make sure to define your variables and summarize your answer in complete sentences. b. Using your equation from (a), can you predict now many boxes can be sold when $50,000 isspent on advertising?c. The company is very ambitious and want to sell 400,000 boxes. How much should they spend onadvertising to achieve their goal?

Answered: A cereal company finds that the number…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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2. A cereal company finds that the number of people who will buy one of its products in the first month
that it is introduced is linearly related. If it spends $40,000, on advertising, then 100,000 boxes of cereal
will be sold. And if it spends $60,000, then 200,000 boxes will be sold.
a. Using the information provided, provide a linear model that describes the company's advertising
scheme. Make sure to define your variables and summarize your answer in complete sentences.

b. Using your equation from (a), can you predict now many boxes can be sold when $50,000 is
spent on advertising?
c. The company is very ambitious and want to sell 400,000 boxes. How much should they spend on
advertising to achieve their goal?

Expert Solution

Given,

Company spends $40,000 on advertising to sell 100,000 boxes of cereal and Company spends $60,000 on advertising to sell 200,000 boxes of cereal.

Therefore required linear equation passes through the points $(40000, 100000) & (60000, 200000)$ .

Now let x and y be the amount spent on advertising and number of boxes of cereal sold respectively. Then the linear equation is,

$y - 100000 = \frac{200000 - 100000}{60000 - 40000} (x - 40000) [∵ Equation of a line passing throught the points (a, b) & (c, d) is y - b = \frac{d - b}{c - a} (x - a)] \Rightarrow y - 100000 = 5 (x - 40000) \Rightarrow y = 5 x - 100000 \Rightarrow y = 5 x - 100000$

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