Green Mountain Sports sells a

full line of outdoor clothing and accessories, including waterproof hiking boots. Due

to competition, Green Mountain can sell these hiking boots for only $$50$ but must

pay suppliers $$37$ per pair. One order is placed per season; excess inventory is sold

at a $50\%$ price discount at the end of the season. At $$50,$ demand over the season

is estimated to follow a Normal distribution with mean $300$ pairs of boots and a

standard deviation of $200.$