$1.$ Flextrola, Inc., an electronics systems integrator, is planning to design a key component for their next$-$generation product with its supplier 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 to Solectrics prior to the beginning of its selling season. Flextrola$$s demand during the season is normally distributed with a mean of $2,000$ and a standard deviation of $300.$ Solectrics$$ production cost for the component is $$40$ per unit, and it plans to sell the component for $$80$ 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 $$120$ each. Flextrola can sell unsold inventory at the end of the season in a secondary electronics market for $$30$ 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.

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a$.$ What is the probability that Flextrola$$s demand will be within $20$ percent of the mean demand value?

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

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For parts c to i$,$ assume that Flextrola orders $1,700$ units.

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c$.$ What is the expected number of lost sales?

d$.$ What is the expected sales quantity?

e$.$ What is the expected number of leftover units?

f$.$ What is the fill rate?

g$.$ What is the stockout probability?

h$.$ What is Flextrola$$s expected profit?

i$.$ What is Solectrics$$ expected profit?