This is a statistics problem using the newsvendor model. You can make $$Georgia Tech Champions$$ T$-$shirts on Friday for $$6$ each to sell after the football

game on Saturday for $$18$ each. However, demand for the T$-$shirts will be zero if Tech loses. If Tech

wins, demand will have a U $[2000,3200]$ distribution. Suppose Tech will win with probability $1/2.$

$($a$)$ Find the number of T$-$shirts to make that maximizes your expected profit, and calculate your

expected profit.

$($b$)$ Find the crystal ball value of knowing whether or not Tech wins.

$($c$)$ Find the crystal ball value of knowing the demand.

$($d$)$ What would your optimal expected profit be if you had to pay a $$5,000$ fee to be permitted

to sell T$-$shirts?

$($e$)$ What would your optimal expected profit be if you had to pay a $$15,000$ fee to be permitted

to sell T$-$shirts?

$($f$)$ Why might maximizing expected profit not be an appropriate objective if this is a one$-$time

business venture for you?

$($g$)$ Same as part $1$a if you can get a $$2$ tax credit for each unsold T$-$shirt by donating them. Use

the formula for the over$/$under problem with salvage value.

$($h$)$ Tell a story that solves part $1$g using the F $1$

D $($x$)=1$ c$/$p formula. Find the number of

T$-$shirts to make but don$$t bother calculating the expected profit.