Chapter 9.3, Problem 34E

To determine

a.

To prove:

The animals tries to adjust its sound to maximize its own satisfaction, there is no solution unless $\frac{a_1}{b_1}=\frac{a_2}{b_2}$ for the given condition $\begin{array}{l}{S}_1=a_1\left(x_1+x_2\right)-b_1{\left(x_1+x_2\right)}^2\text{ and}\\ {\text{S}}_2=a_2\left(x_1+x_2\right)-b_2{\left(x_1+x_2\right)}^2\end{array}$.

To determine

b.

To prove:

The expression $x_1+x_2=\frac{a_1+a_2}{2\left(b_1+b_2\right)}$ for the given condition, $\begin{array}{l}{S}_1=a_1\left(x_1+x_2\right)-b_1{\left(x_1+x_2\right)}^2\text{ and}\\ {\text{S}}_2=a_2\left(x_1+x_2\right)-b_2{\left(x_1+x_2\right)}^2\end{array}$.