Flextrola, Inc., an electronics systems integrator, is planning to design a key component for its next$-$generation product with Solectrics. Flextrola will integrate the component with

some software and then sell it to consumers. Given the short life cycles of such products and the long lead times quoted by Solectrics, Flextrola only has one opportunity to place an

order with Solectrics prior to the beginning of its selling season. Flextrola's demand during the season is normally distributed with a mean of $950$ and a standard deviation of $575.$ Solectrics' production cost for the component is $$52$ per unit, and it plans to sell the component for $$72$ per unit to Flextrola. Flextrola incurs essentially no cost associated

with the software integration and handling of each unit. Flextrola sells these units to consumers for $$121$ each. Flextrola can sell unsold inventory at the end of the season in

a secondary electronics market for $$50$ each. The existing contract specifies that once Flextrola places the order, no changes are allowed to it$.$ Also, Solectrics does not accept

any returns of unsold inventory, so Flextrola must dispose of excess inventory in the secondary market.

a$.$ What is the probability that Flextrola's demand will be within $20$ percent of its forecast $($mean demand$)?$

b$.$ What is the probability that Flextrola's demand will be more than $45$ percent greater than Flextrola's forecast

$($mean demand$)?$

c$.$ Under this contract, how many units should Flextrola order to maximize its expected profit?

d$.$ What is the cost of uncertainty in demand?

e$.$ If Flextrola orders $1500$ units, how many units of inventory can Flextrola expect to sell in the secondary electronics market?

f$.$ If Flextrola orders $1500$ units, what are expected sales?

G$.$If Flextrola orders $1500$ units, what is expected profit?