Answer
a. $Y(x)=\begin{cases} 50, \hspace{1.4cm} x\leq30 \\ 95-1.5x,\ x\gt30 \end{cases}$
b. $T(x)=\begin{cases} 50x, \hspace{1.6cm} x\leq30 \\ 95x-1.5x^2,\ x\gt30 \end{cases}$
Work Step by Step
a. Based on the given conditions, we can express the yield per tree as $Y(x)=\begin{cases} 50, \hspace{2.7cm} x\leq30 \\ 50-1.5(x-30),\ x\gt30 \end{cases}$ or $Y(x)=\begin{cases} 50, \hspace{1.4cm} x\leq30 \\ 95-1.5x,\ x\gt30 \end{cases}$
which gives $Y(30)=50\ lb$ and an average rate of decrease of 1.5 pounds per additional tree over 30 per acre.
b. Based on the above results, we can express the total yield per acre as
$T(x)=\begin{cases} 50x, \hspace{1.6cm} x\leq30 \\ 95x-1.5x^2,\ x\gt30 \end{cases}$
