You are the procurement manager of Tacy$$s$.$ The supplier offers a new style of classical bomber

jacket for the winter season. The purchase cost is $$200,$ and the selling price is $$500.$ You

consider offering a discount for unsold jackets at the end of the season. The discounted price is

$$150.$ The forecasted demand, D$,$ is normally distributed with a mean of $3,000$ units $(\backslash$mu $)$ and a

standard deviation of $700$ units $(\backslash$sigma $).$ Assume that the A$/$F ration is $1.$

$($a$)$ You will get a promotion if the total sold jackets is above $4,000$ units. What is the probability

that the actual demand will be $4,000$ units or more?

$($b$)$ Selling less than $80\%$ of the average forecast may result in the placement of your position

in a lower pay grade. What is the probability of selling more than $80\%?$

$($c$)$ What is the probability that the actual demand is within $25\%$ of the average forecast?

$($d$)$ What is the expected profit maximizing order quantity, Q$?$

$($e$)$ Assuming Tacy$$s Manger enforces and orders quantity of Q$=4,500.$ What are the expected

lost sales?