# Confusing Piecewise function

• February 15th 2011, 04:50 PM
somanyquestions
Confusing Piecewise function
The annual yield per walnut tree is fairly constant at 60 pounds per tree when the number of trees per acre is 20 or fewer.
For each additional tree over 20, the annual yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding.
How many walnut trees should be planted per acre to maximize the annual yield for the acre? What is the maximum number of pounds of walnuts per acre?

from what i assumed i set this up.

x= the number of trees per acre

f(x)= { 60x if x is less than or equal to 20}
{ 60x-2(x-20) if x is greater than 20}

i'm not sure if this is right or where to go from here.
• February 15th 2011, 11:33 PM
earboth
Quote:

Originally Posted by somanyquestions
The annual yield per walnut tree is fairly constant at 60 pounds per tree when the number of trees per acre is 20 or fewer.
For each additional tree over 20, the annual yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding.
How many walnut trees should be planted per acre to maximize the annual yield for the acre? What is the maximum number of pounds of walnuts per acre?

from what i assumed i set this up.

x= the number of trees per acre

f(x)= { 60x if x is less than or equal to 20}
{ 60x-2(x-20) if x is greater than 20}

i'm not sure if this is right or where to go from here.

1. The 2nd term of the function is not correct: Let x denote the number of trees if it is greater than 20

$\underbrace{(60-2(x-20))}_{yield\ per\ tree} \underbrace{x}_{number\ of\ trees}$

2. The complete function looks like that:

$f(x)=\left\{\begin{array}{rcl}60 x&if& x \leq 20\\ 100x - 2x^2 & if & 20 < x \leq 50 \end{array}\right.$