Holt Mcdougal Larson Algebra 2: Student Edition 2012

1st Edition

ISBN: 9780547647159

Author: HOLT MCDOUGAL

Publisher: HOLT MCDOUGAL

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Expert Solution & Answer

Chapter 2.5, Problem 44PS

Solution

(a)

Write an expression for the company’s total revenue in terms of x .

The expression revenue in terms of x is given by 40x−4x3 .

Given:

The price p is given as p=40−4x2 , where x is the number in millions.

Calculation:

It has been given that p=40−4x2 .

Therefore, the revenue is given by

R=px=40−4x2x=40x−4x3

Hence, the expression revenue in terms of x is given by 40x−4x3 .

(b)

Write a function for the company’s profit P to make x radios.

The profit function given by Px=−4x3+25x .

Given:

The price p is given as p=40−4x2 , where x is the number in millions.

Rx=40x−4x3

The cost of making one radio is $15.

Calculation:

It has been given that Rx=40x−4x3 .

Cost of making one radio is $15.

Hence, the cost of making x radios is given by 15x .

Therefore, the profit function is given by

Px=Rx−Cx=−4x3+25x

(c)

Write and solve an equation to find a lesser number of radios that the company could produce and still make the same profit.

The company could produce 1.386 million radios to generate the same profit.

Given:

The profit function given by Px=−4x3+25x .

The company produces 1.5 million of radios and generate a profit of $24,000,000.

Calculation:

It has been given that Px=−4x3+25x .

For the profit to be $24,000,000.

24=−4x3−25x

In order to find the values for x, graph the equations y=24,y=40x−4x3−15x in the same coordinate axis and the positive value of x-coordinate of the intersection point will be the number of radios that company will produce.

The positive x-value other than 1.5 is 1.386 .

So, the company could produce 1.386 million radios to generate the same profit.

(d)

Do all the solutions in part c makes sense. Explain.

All these solutions don’t make sense. Only the positive values of x will give the number of radios to generate a profit of $24,000,000.

Given:

The profit function given by Px=−4x3+25x .

The company produces 1.5 million of radios and generate a profit of $24,000,000.

Calculation:

It has been given that Px=−4x3+25x .

For the profit to be $24,000,000.

24=−4x3−25x

In order to find the values for x, graph the equations y=24,y=−4x3−25x in the same coordinate axis and the values of x-coordinate of the intersection points will be the number of radios that company will produce.

From the graph, there are three solutions

x=1.5,x=1.386,x=−2.886 .

Hence, the solution x=−2.886 is not possible because the number of radios cannot be negative.

Therefore, all these solutions don’t make sense. Only the positive values of x will give the number of radios to generate a profit of $24,000,000.

Chapter 2.5, Problem 43PS

Chapter 2.5, Problem 45PS

Chapter 2 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 2.1 - Prob. 1GP Ch. 2.1 - Prob. 2GP Ch. 2.1 - Prob. 3GP Ch. 2.1 - Prob. 4GP Ch. 2.1 - Prob. 5GP Ch. 2.1 - Prob. 6GP Ch. 2.1 - Prob. 7GP Ch. 2.1 - Prob. 8GP Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E

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