$($ii$)$ To maximize the supply chain$$s total profit $($SJ$$s profit plus Cusano$$s profit$),$ how many grills

should be shipped to Cusano$$s hardware? $(10$ points$)$

$($a$)5\mathrm{.}79$

$($b$)8\mathrm{.}03$

$($c$)10\mathrm{.}00$

$($d$)11\mathrm{.}23$

$($e$)14\mathrm{.}21$

$($iii$)$ Suppose SJ and Cusano agree on the following revenue sharing contract: the wholesale price is $$80$

$($as opposed to $$185$ in the original contract$)$ and the per$-$unit revenue of $$250$ is shared with SJ; that is$,$

Cusano keeps $$250(1-$y$)$ and SJ keeps $$250$y of the revenue per grill. To achieve the first$-$best profit in

part b$,$ what should y be$?(10$ points$)$

$($a$)0\mathrm{.}2$

$($b$)0\mathrm{.}4$

$($c$)0\mathrm{.}6$

$($d$)0\mathrm{.}8$

$($e$)1\mathrm{.}0$