Answer
.
Work Step by Step
The yield per tree would be the difference between the original yield per tree and increase in yield per tree.
$\left[ \text{Yield per tree} \right]=\text{ }\left[ \text{Original yield} \right]-\left[ \text{decrease in yield of lemons} \right]$
Substitute $Y\left( x \right)$ for yield per tree, $320$ for original yield and $4\left( x-50 \right)$ for $\text{decrease in yield of lemons}$.
$\begin{align}
& Y\left( x \right)=320-4\left( x-50 \right) \\
& =320-4x+200 \\
& =520-4x
\end{align}$
Hence, the expression for the yield per tree Y as a function of yield per tree x is $Y\left( x \right)=520-4x$.
(b)
Numbers of lemons per acre will be the yield per tree times the number of trees per acre.
$\left[ \text{yield per acre} \right]=\text{ }\left[ \text{yield per tree} \right]\left[ \text{number of trees per acre} \right]$
From part (a), the expression for the yield per tree Y as a function of yield per tree x is
$Y\left( x \right)=520-4x$.
Substitute $T\left( x \right)$ for yield per acre, $520-4x$ for yield per tree and x for number of trees per acre.
$\begin{align}
& T\left( x \right)=\left( 520-4x \right)x \\
& =520x-4{{x}^{2}} \\
& =-4{{x}^{2}}+520x
\end{align}$
Hence, the expression for the yield per acre T as a function of the tress per acre x is $T\left( x \right)=-4{{x}^{2}}+520x$.
