A designer brand, Bamino, is making a production decision for a limited collection of handbags to be sold at its store during the next two months. The variable cost to produce each handbag is $$120.$ The handbag will be sold at the store for $$300$ during the selling season. After that, any unsold handbags will be sold at an outlet store at $75\%$ discount from the original price tag, and it is expected that all remaining handbags can be sold at the outlet store.

The distribution of demand for the handbag during the selling season is given below. Demand

$36$

$37$

$38$

$39$

$40$ Probability

$0\mathrm{.}1$

$0\mathrm{.}15$

$0\mathrm{.}4$

$0\mathrm{.}2$

$0\mathrm{.}15$