Problem $5(10$pt$)$ Two alternative designs are under consideration for a tapered fas$-$

tening pin. The fastening pins are sold for $$0\mathrm{.}70$ each. Either design will serve equally

well and will involve the same material and manufacturing cost except for the lathe and

drill operations. Design A will require $16$ hours of lathe time and $4\mathrm{.}5$ hours of drill time

per $1,000$ units. Design B will require $7$ hours of lathe time and $12$ hours of drill time per

$1,000$ units. The variable operating cost of the lathe, including labor, is $$18\mathrm{.}60$ per hour.

The variable operating cost of the drill, including labor, is $$16\mathrm{.}90$ per hour. Finally, the

firm has made preliminary research on both Design A $($which has incurred $$5,000)$ and

Design B $($which has incurred $$9,000).$

$($a$)(5$pt$).$ Which design should be adopted if $125,000$ units are sold each year?

$($b$)(5$pt$).$ What is the annual saving over the other design?