a$)$ Over the past $5$ weeks, demand for wine at Winston$$s Winery has been $4200,3300,1700,2900,$ and $800$ bottles. Winston has placed weekly orders for glass bottles of $3000,5000,1500,3100,$ and $500$ units.

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I. What is the variance of demand for Winston$$s Winery?

II$.$ What is the variance of orders from Winston$$s Winery for glass bottles?

III. What is the bullwhip measure for glass bottles for Winston$$s Winery?

IV$.$ Is Winston$$s Winery providing an amplifying or smoothing effect?

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b$)$Century Outlet has total end$-$of$-$year assets of $$20$ million. The first$-$of$-$the$-$year inventory was $$900,000,$ with a year$-$end inventory of $$1,100,000.$The annual revenue was $$25$ million and the annual cost of goods sold was $$15$ million. The owner wants to evaluate his supply chain performance. $$Pease calculate the following SC performance measures:

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I. Gross Margin Percentage $=$

II$.$ Average Inventory Investment $=$

III. Percentage of Assets invested in inventory $=$

IV$.$ Inventory turnover $=$

V$.$ Weeks of supply $=$

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c$)$ The fixed costs for operating our plant at locations A$,$ B$,$ and C$,$ D are $$1600,$ $$2300,$ $$2,500,$ and $$6,000$ per day respectively. $$The variable costs are $$8,$ $$9,$ $$5,$ and $$3$ per unit respectively. $$Find the range of production level where each location is optimal.

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d$)$ We are trying to lease a warehouse for the next four years. $$ Option $1$ is to pay a non$-$refundable deposit of $$40,000$ now and then $$3,100$ per month at the end of each month for the next four years. $$ Another option is to pay one month rent of $$3,900$ at the beginning of each month for the next four years and a security deposit of $$3,600$ now which will be returned at the end of the lease period. $$Find the present value of each option using an interest rate of $7\%$ per year.