PA $13-8($Algo$)$ Geoff Gullo owns a small firm that manufactures...

Geoff Gullo owns a small firm that manufactures "Gullo Sunglasses". He has the opportunity to sell a particular seasonal model to Land's Start, a catalog retailer. Geoff offers Land's Start two purchasing options. Use Table $13\mathrm{.}4.$

Option $1$: Geoff offers to set his price at $$68$ and agrees to credit Land's Start $$51$ for each unit Land's Start returns to Geoff at the end of the season $($because those units did not sell$).$ Because styles change each year, there is essentially no value in the returned merchandise.

Option $2$: Geoff offers a price of $$58$ for each unit, but returns are no longer accepted. In this case, Land's Start throws out unsold units at the end of the season.

This season's demand for this model will be normally distributed with a mean of $150$ and a standard deviation of $75.$ Land's Start will sell those sunglasses for $$105$ each. feoff's unit production cost is $$21.$

Note: If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then credit for a correct answer will depend on using the specified method.

a$.$ How much would Land's Start buy if it chose option $1?$ Use Table $13\mathrm{.}4$ and round$-$up rule.

Note: Round your answer up to a whole number.

Order quantity

b$.$ How much would Land's Start buy if it chose option $2?$ Use Table $13\mathrm{.}4$ and round$-$up rule.

Note: Round your answer up to a whole number.

Order quantity

c$.$ Use Table $13\mathrm{.}4.$ Which option will Land's Start choose? Complete the table below:

Note: Use your rounded order quantities from Parts a & b$.$ Round your "Expected Inventory and Expected Sales" to $2$ decimal places.

$\backslash$table$[[,$Option $1,$Option $2],[$Expected Inventory,,$],[$Expected sales,,$],[$Expected profit,,$]]$

d$.$ Suppose Land's Start chooses option $1$ and orders $250$ units. What is Geoff Gullo's expected profit? Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Do not round intermediate calculations. Round your answer up to a whole number.

Expected profit