$(15$ Points$)$ A county $is$ considering three locations for a new dam. The three

alternatives for the dams for the three locations cost $$25,000,000\mathrm{.}00,$

$$30,000,000\mathrm{.}00,$ and $$32,000,000\mathrm{.}00.$ Currently flood damage amounts $to$

$$20,000,000\mathrm{.}00$ per year. $If$ the new dams are built, the flood damage will $be$

reduced $to$ $$17,000,000\mathrm{.}00$;$$16,000,000\mathrm{.}00$; and $$15,500,000\mathrm{.}00$ per year,

respectively. Use $an$ interest rate $of6\%$ and a life $of10$ years.

$a.$ Calculate the benefit $of$ each alternative.

$b.$ Calculate the conventional $\frac{B}{C}$ ratio $of$ each alternative.

$c.$ Determine which dam should $be$ built based $on$ the incremental

benefi$\frac{t}{cost\text{r}\text{a}\text{t}\text{i}\text{o}\text{s}\text{.}}$