Answer
See below:
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, $270$ for original yield and $3\left( x-30 \right)$ for $\text{decrease in yield of lemons}$.
$\begin{align}
& Y\left( x \right)=270-3\left( x-30 \right) \\
& =270-3x+90 \\
& =360-3x
\end{align}$
Hence, the expression for the yield per tree Y as a function of yield per tree x is $Y\left( x \right)=360-3x$.
(b)
Numbers of oranges 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 $Y\left( x \right)=360-3x$.
Substitute $T\left( x \right)$ for yield per acre, $360-3x$ for yield per tree and x for number of trees per acre.
$\begin{align}
& T\left( x \right)=\left( 360-3x \right)x \\
& =360x-3{{x}^{2}} \\
& =-3{{x}^{2}}+360x
\end{align}$
Hence, the expression for the yield per acre T as a function of the trees per acre x is $T\left( x \right)=-3{{x}^{2}}+360x$.
