# The number of trees should be planted per acre to obtain the maximum yield of apples.

### Precalculus: Mathematics for Calcu...

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

### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 3.1, Problem 69E
To determine

## To evaluate: The number of trees should be planted per acre to obtain the maximum yield of apples.

Expert Solution

The number of trees should be planted per acre to obtain the maximum yield of apples is 50trees/acre .

### Explanation of Solution

Given:

The number of apples produced per acre is given by the function A(n)=n(9009n) , where n is the number of trees per acre.

Calculation:

The function of the number of apples produced per acre is given by

A(n)=n(9009n)=900n9n2=9n2+900n (1)

The standard form of function,

f(n)=an2+bn+c (2)

The maximum or minimum value of the function occurs at,

n=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=9b=900

Substitute 9 for a and 900 for b in the equation (3),

n=9002×9=90018=50

The number of trees per acre is 50 .

The function has maximum value,

a=9<0 .

Thus, the number of trees should be planted per acre to obtain the maximum yield of apples is 50trees/acre .

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