Question

Optimization problem.

Answer 1

See file.

Answer 2

I will use symmetry....lots of it. Here we go,

\[(a)\;\;\;\;\;\;AB \equiv -2x+34 \]
\[(b)\;\;\;\;\;\; A_{area}=width*height \;\;\;\;\rightarrow \;\;\;\;\;\;\;\;\;\;\;\;\;(2x)(-2x+34)\]

I used symmetry for width....look at the picture.
\[(c)\;\;\;\;\;\; A_{area}=-4x^{2}+68x \;\;\;\;\;\; \rightarrow \;\;\;\;\;\;\;\;\;\; A_{area}=-4x^{2}+68x\]
\[\;\;\;\;\;\; A_{area}^{\prime}=-8x+68 \]
\[\;\;\;\;\;\; 0=-8x+68 \]
\[\;\;\;\;\;\; x=\frac{68}{8} \rightarrow \frac{17}{2}\]

So Width=2(17/2)=17 and height=-2(17/2)+34=-17+34=17