Question $3.(22$ points$)$

Eagles Flora is a fresh flower shop in Washington DC$.$ The manager of the shop is deciding how many bouquets of fresh flowers to order for the upcoming weekend. The flowers are used to create beautiful arrangements that are in high demand, but the shop has experienced fluctuations in demand in the past due to factors such as seasonal changes and local events.

Using historical data and expert judgment, the flower shop estimates that the demand for the weekend is normally distributed with a mean of $200$ bouquets and a standard deviation of $50$ bouquets. Each bouquet is sold for $$40.$ The manager has two suppliers for the fresh flowers with the following offerings:

Supplier A: It costs the supplier $$10$ per bouquet to provide fresh flowers. The supplier sells each bouquet to the shop at $$20.$ If there are any unsold bouquets, the supplier buys them back at $$5$ per bouquet and composts it at no cost$.$

Supplier B: It costs the supplier $$12$ per bouquet to provide fresh flowers. The supplier sells each bouquet to the shop at $$24.$ If there are any unsold bouquets, the supplier buys them back at $$8$ per bouquet and sells the returned flowers as organic compostable material for $$1$ per bouquet.

Both suppliers only prepare as many bouquets as the flower shop orders $--$ nothing more, nothing less.

The manager will order the flower from only one of these suppliers. Answer the following questions based on the information provided. Use the Excel spreadsheet for the Newsvendor Problem, if$/$when needed.

a$)$ Analysis for Supplier A: The manager will use the newsvendor model to determine how many bouquets to order from Supplier A for the weekend. The manager is interested in maximizing the expected profits. Complete Table Q$3-$A$.$ You must show all the work you do as you calculate each value. You can also use Excel to carry out the calculations. Compute the parameters or the performance with respect to the flower shop's inventory decisions and inventory performance, unless noted otherwise.

b$)(10$ points$)$ Analysis for Supplier B: The manager will use the newsvendor model to determine how many bouquets to order from Supplier B for the weekend. The manager is interested in maximizing the expected profits. Complete Table Q$3-$B$.$ You must show all the work you do as you calculate each value. You can also use Excel to carry out the calculations. Compute the parameters or the performance with respect to the flower shop's inventory decisions and inventory performance, unless noted otherwise.

c$)(2$ points$)$ Which option is better for the flower shop? Discuss by providing any numbers necessary based on your analysis in parts a and b$.$

NOTE$-1$: SHOW ALL YOUR WORK. USE $4$ DECIMAL PLACES IN ALL CALCULATIONS. MAKE SURE YOU CLEARLY LABEL AND HIGHLIGHT YOUR ANSWERS TO EACH QUESTION.TABLE Q$3-$A: Newsvendor problem with Supplier A

$\backslash$table$[[$Unit cost of underage for the flower shop $(0\mathrm{.}5$ points$),],[$Unit cost of overage for the flower shop $(0\mathrm{.}5$ points$),],[$Critical ratio for the newsvendor $(0\mathrm{.}5$ points$),],[$Optimal newsvendor quantity $(2$ points$),],[\backslash$table$[[$Expected amount of lost sales when the optimal newsvendor quantity is used$],[$ points$)]],],[\backslash$table$[[$Expected amount of goods sold when the optimal newsvendor quantity is used$],[(0\mathrm{.}5$ points$)]],],[\backslash$table$[[$Expected amoung of unsold inventory when the optimal newsvendor quantity is$],[$used $(0\mathrm{.}5$ points$)]],],[\backslash$table$[[$Expected sales revenue when the optimal newsvendor quantity is used $(0\mathrm{.}5],[$points$)]],],[\backslash$table$[[$Expected cost of purchasing the goods from the supplier when the optimal$],[$newsvendor quantity is used $(0\mathrm{.}5$ points$)]],],[\backslash$table$[[$Expected salvage value when the optimal newsvendor quantity is used $(0\mathrm{.}5],[$points$)]],],[$Expected optimal profit of the newsvendor $(1$ point$),],[$Expected fill rate when the optimal newsvendor quantity is used $(0\mathrm{.}5$ points$),],[\backslash$table$[[$Expected in$-$stock probability of the product when the optimal newsvendor$],[$quantity is used $(0\mathrm{.}5$ points$)]],],[\backslash$table$[[$Expected out$-$of$-$stock probability of the product when the optimal newsvendor$],[$quantity is used $(0\mathrm{.}5$ points$)]],],[\backslash$table$[[$Supplier A$\text{'}$s expected profit when the flower shop orders the optimal$],[$newsvendor quantity $(1$ point$)]],],[$TABLE Q$3-$B: Newsvendor problem with Supplier B$,],[$Unit cost of underage for the flower shop $(0\mathrm{.}5$ points$),],[$Unit cost of overage for the flower shop $(0\mathrm{.}5$ points$),],[$Critical ratio for the newsvendor $(0\mathrm{.}5$ points$),],[$Optimal newsvendor quantity $(2$ points$),],[\backslash$table$[[$Expected amount of lost sales when the optimal newsvendor quantity is used$],[$ points$)]],],[\backslash$table$[[$Expected amount of goods sold when the optimal newsvendor quantity is used$],[(0\mathrm{.}5$ points$)]],],[\backslash$table$[[$Expected amoung of unsold inventory when the optimal newsvendor quantity is$],[$used $(0\mathrm{.}5$ points$)]],],[\backslash$table$[[$Expected sales revenue when the optimal newsvendor quantity is used $(0\mathrm{.}5],[$points$)]],],[\backslash$table$[[$Expected cost of purchasing the