BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 3.1, Problem 65E
To determine

To evaluate: The maximum revenue and the amount of unit manufactured to obtain this maximum.

Expert Solution

Answer to Problem 65E

The maximum revenue and the amount of unit manufactured to obtain this maximum is $4000 and 100units respectively.

Explanation of Solution

Given:

The revenue generated by selling x unit of certain commodity is given by the function R(x)=80x0.4x2 , where R(x) measured in dollars.

Calculation:

The revenue generated by selling x units is given by the function

R(x)=80x0.4x2=0.4x2+80x (1)

The standard form of function,

f(x)=ax2+bx+c (2)

The maximum or minimum value of the function occurs at,

x=b2a (3)

If a>0 , then the minimum value is f(b2a) .

If a<0 , then the maximum value is f(b2a) .

From the equation (1) and (2),

a=0.4b=80

Substitute 0.4 for a and 80 for b in the equation (3),

x=802×(0.4)=800.8=100

The amount of manufactured to obtain the maximum revenue is 100units .

The function has maximum value,

a=0.4<0 .

The maximum value of the function at x=100 ,

R(100)=80×1000.4×1002=80004000=4000

The maximum value of the function R(x)=80x0.4x2 is 4000 .

The maximum revenue is 4000dollars .

Thus, the maximum revenue and the amount of unit manufactured to obtain this maximum is $4000 and 100units respectively.

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