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 $$63$ and agrees to credit Land$$s Start $$53$ for each unit Land$$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 $$53$ for each unit, but returns are no longer accepted. In this case, Land$$s Start throws out unsold units at the end of the season.

This season$$s demand for this model will be normally distributed with a mean of $150$ and a standard deviation of $125.$ Land$$s Start will sell those sunglasses for $$95$ each. Geoff$$s unit production cost is $$22.$

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.

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.

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.

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.

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.