Problem $1.$ ABC is a retailer that carries Easter eggs. The entire demand for Easter eggs

occurs within a few days of Easter. ABC buys the eggs from a supplier at $$c$ per egg and

sells them at $$p$ per egg. After Easter, the supplier buys back a fraction $f$ of unsold eggs

at $$b$ per egg. $($For example, if $f=0\mathrm{.}4$ and $\frac{?}{\text{A}\text{B}\text{S}}$ ends up with $100$ unsold eggs, then the

supplier will pay ABC$40b.)$ The remaining fraction, $1-f,$ of unsold eggs goes to waste.

Assume that $(c_u)(c_o)c$;$p$;$bfp=10$;$c=4$;$b=2f=0\mathrm{.}5b.$

$(a)$ What $is$ the unit underage cost for Easter eggs $(c_u)?$ How about the unit overage cost

$(c_o)?$ What $is$ the critical fractile? $(Your$ answer should $bein$ terms $ofc$;$p$;$b$; and $f.)$

$(b)$ Suppose that $p=10$;$c=4$;$b=2$; and $f=0\mathrm{.}5.$ Also, assume that the demand for

Easter eggs $is$ given $by$ the following discrete demand distribution.

How many eggs should ABC stock?

$(c)$ What $is$ the expected number $of$ eggs that ABC will sell $to$ the consumers? What $is$ the

expected number $of$ eggs that will $be$ left over?

$(d)$ What $is$ ABC's expected profit?