Question $2($Normally Distributed Demand$)$

The Supermarket Store is about to place an order for Halloween candy. One best$-$selling

brand of candy can be purchased for $c=$$$4\mathrm{.}50$ per box before and up to Halloween.

After Halloween, all the remaining candy can be marked down and sold for $v=$$$0\mathrm{.}75$

per box. Assume that the unit loss in goodwill stemming from customers whose demand

is not satisfied is $B=$$$0\mathrm{.}50.$

Through an assessment of the consumer market for the candy, the store manager, not

surprising, find that market demand is sales price dependent and uncertain. For three

potential sales prices, the manager estimates that demand is normally distributed with the

following parameters:

Sales price $p=$$$7\mathrm{.}50$; mean $=37\mathrm{.}60$; and standard deviation $=2\mathrm{.}94.$

Sales Price $p=$$$10\mathrm{.}50$; mean $=34\mathrm{.}90$; and standard deviation $=2\mathrm{.}74.$

Sales Price $p=$$$13\mathrm{.}50$; mean $=33\mathrm{.}20$; and standard deviation $=2\mathrm{.}48.$

For each sales price, complete the following table: