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 $$52$ for each unit Land$$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$$s demand for this model will be normally distributed with a mean of $200$ and a standard deviation of $75.$ Land$$s Start will sell those sunglasses for $$105$ each. Geoff$$s unit production cost is $$23.$

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$$s Start chooses option $1$ and orders $300$ units. What is Geoff Gullo$$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.

TABLE $13\mathrm{.}4$

The Distribution $,$ F$($Q$),$ and Expected Inventory, I$($Q$),$ Functions for the Standard Normal Distribution

Function

z F$($z$)$ I$($z$)$

$-4\mathrm{.}00\mathrm{.}00000\mathrm{.}0000$

$-3\mathrm{.}90\mathrm{.}00000\mathrm{.}0000$

$-3\mathrm{.}80\mathrm{.}00010\mathrm{.}0000$

$-3\mathrm{.}70\mathrm{.}00010\mathrm{.}0000$

$-3\mathrm{.}60\mathrm{.}00020\mathrm{.}0000$

$-3\mathrm{.}50\mathrm{.}00020\mathrm{.}0001$

$-3\mathrm{.}40\mathrm{.}00030\mathrm{.}0001$

$-3\mathrm{.}30\mathrm{.}00050\mathrm{.}0001$

$-3\mathrm{.}20\mathrm{.}00070\mathrm{.}0002$

$-3\mathrm{.}10\mathrm{.}00100\mathrm{.}0003$

$-3\mathrm{.}00\mathrm{.}00130\mathrm{.}0004$

$-2\mathrm{.}90\mathrm{.}00190\mathrm{.}0005$

$-2\mathrm{.}80\mathrm{.}00260\mathrm{.}0008$

$-2\mathrm{.}70\mathrm{.}00350\mathrm{.}0011$

$-2\mathrm{.}60\mathrm{.}00470\mathrm{.}0015$

$-2\mathrm{.}50\mathrm{.}00620\mathrm{.}0020$

$-2\mathrm{.}40\mathrm{.}00820\mathrm{.}0027$

$-2\mathrm{.}30\mathrm{.}01070\mathrm{.}0037$

$-2\mathrm{.}20\mathrm{.}01390\mathrm{.}0049$

$-2\mathrm{.}10\mathrm{.}01790\mathrm{.}0065$

$-2\mathrm{.}00\mathrm{.}02280\mathrm{.}0085$

$-1\mathrm{.}90\mathrm{.}02870\mathrm{.}0111$

$-1\mathrm{.}80\mathrm{.}03590\mathrm{.}0143$

$-1\mathrm{.}70\mathrm{.}04460\mathrm{.}0183$

$-1\mathrm{.}60\mathrm{.}05480\mathrm{.}0232$

$-1\mathrm{.}50\mathrm{.}06680\mathrm{.}0293$

$-1\mathrm{.}40\mathrm{.}08080\mathrm{.}0367$

$-1\mathrm{.}30\mathrm{.}09680\mathrm{.}0455$

$-1\mathrm{.}20\mathrm{.}11510\mathrm{.}0561$

$-$l$\mathrm{.}10\mathrm{.}13570\mathrm{.}0686$

$-1\mathrm{.}00\mathrm{.}15870\mathrm{.}0833$

$-0\mathrm{.}90\mathrm{.}18410\mathrm{.}1004$

$-0\mathrm{.}80\mathrm{.}21190\mathrm{.}1202$

$-0\mathrm{.}70\mathrm{.}24200\mathrm{.}1429$

$-0\mathrm{.}60\mathrm{.}27430\mathrm{.}1687$

$-0\mathrm{.}50\mathrm{.}30850\mathrm{.}1978$

$-0\mathrm{.}40\mathrm{.}34460\mathrm{.}2304$

$-0\mathrm{.}30\mathrm{.}38210\mathrm{.}2668$

$-0\mathrm{.}20\mathrm{.}42070\mathrm{.}3069$

$-0\mathrm{.}10\mathrm{.}46020\mathrm{.}3509$

$0\mathrm{.}00\mathrm{.}50000\mathrm{.}3989$

$0\mathrm{.}10\mathrm{.}53980\mathrm{.}4509$

$0\mathrm{.}20\mathrm{.}57930\mathrm{.}5069$

$0\mathrm{.}30\mathrm{.}61790\mathrm{.}5668$

$0\mathrm{.}40\mathrm{.}65540\mathrm{.}6304$

$0\mathrm{.}50\mathrm{.}69150\mathrm{.}6978$

$0\mathrm{.}60\mathrm{.}72570\mathrm{.}7687$

$0\mathrm{.}70\mathrm{.}75800\mathrm{.}8429$

$0\mathrm{.}80\mathrm{.}78810\mathrm{.}9202$

$0\mathrm{.}90\mathrm{.}81591\mathrm{.}0004$

$1\mathrm{.}00\mathrm{.}84131\mathrm{.}0833$

$1\mathrm{.}10\mathrm{.}86431\mathrm{.}1686$

$1\mathrm{.}20\mathrm{.}88491\mathrm{.}2561$

$1\mathrm{.}30\mathrm{.}90321\mathrm{.}3455$

$1\mathrm{.}40\mathrm{.}91921\mathrm{.}4367$

$1\mathrm{.}50\mathrm{.}93321\mathrm{.}5293$

$1\mathrm{.}60\mathrm{.}94521\mathrm{.}6232$

$1\mathrm{.}70\mathrm{.}95541\mathrm{.}7183$

$1\mathrm{.}80\mathrm{.}96411\mathrm{.}8143$

$1\mathrm{.}90\mathrm{.}97131\mathrm{.}9111$

$2\mathrm{.}00\mathrm{.}97722\mathrm{.}0085$

$2\mathrm{.}10\mathrm{.}98212\mathrm{.}1065$

$2\mathrm{.}20\mathrm{.}98612\mathrm{.}2049$

$2\mathrm{.}30\mathrm{.}98932\mathrm{.}3037$

$2\mathrm{.}40\mathrm{.}99182\mathrm{.}4027$

$2\mathrm{.}50\mathrm{.}99382\mathrm{.}5020$

$2\mathrm{.}60\mathrm{.}99532\mathrm{.}6015$

$2\mathrm{.}70\mathrm{.}99652\mathrm{.}7011$

$2\mathrm{.}80\mathrm{.}99742\mathrm{.}8008$

$2\mathrm{.}90\mathrm{.}99812\mathrm{.}9005$

$3\mathrm{.}00\mathrm{.}99873\mathrm{.}0004$

$3\mathrm{.}10\mathrm{.}99903\mathrm{.}1003$

$3\mathrm{.}20\mathrm{.}99933\mathrm{.}2002$

$3\mathrm{.}30\mathrm{.}99953\mathrm{.}3001$