Answer
(a) $8x+\frac{7200}{x}$
(b) $30ft$
(c) $[15,60]$ft
Work Step by Step
(a) Use the assignment in problem figure, the side length adjacent to the road is $x$.
As the total area is $1200ft^2$, the length of the other side is $\frac{1200}{x}$, and
the total cost would be $C=5x+3x+3\times2\times\frac{1200}{x}=8x+\frac{7200}{x}$
(b) Rewrite the equation as $C=8(x+\frac{900}{x})$, and the minimum cost can be found
as $C=8\times60=480$dollars, when $x=30ft$
(c) Let the total cost be 600 dollars, we have $8x+\frac{7200}{x}\leq 600$ and a solution can
be found as shown in the graph, $x\in[15,60]$ft.
