Problem $3$: $10$ points Cunningham Products is evaluating five possible locations to build a distribution center. Data estimated from the accounting department are provided below. The annual production is estimated to be $30,000$ units. Cunningham Products Location Analysis: DATA Locat. $1$ Locat. $2$ Locat. $3$ Locat. $4$ Locat. $5$ Fixed costs $$80,000$ $$110,000$ $$109,000$ $$135,000$ $$110,000$ Direct Material$/$unit $$4\mathrm{.}22$ $$4\mathrm{.}65$ $$5\mathrm{.}05$ $$4\mathrm{.}80$ $$4\mathrm{.}80$ Direct labor$/$ unit $$12\mathrm{.}40$ $$13\mathrm{.}50$ $$11\mathrm{.}60$ $$15\mathrm{.}40$ $$13\mathrm{.}80$ Overhead$/$unit $$2\mathrm{.}50$ $$2\mathrm{.}20$ $$2\mathrm{.}20$ $$2\mathrm{.}70$ $$2\mathrm{.}00$ Transportation cost$/$unit $$0\mathrm{.}40$ $$0\mathrm{.}70$ $$0\mathrm{.}30$ $$0\mathrm{.}84$ $$0\mathrm{.}71$ a$)$ Which location provides the least cost? b$)$ For what range of demand would each location be best? $($Hint: Slides $25,26$ for Break$-$even analysis$)$