PART A: Suppose that a liquor distributor has an average known weekly demand of 10000 units of 1 Liter Makers Mark Bourbon. Each bottle of Makers Mark costs the distributor $25 per bottle. Specifically for the space for this product, it costs the distributor $0.50 per bottle per week to hold in inventory. When the distributor purchases from the manufacturer, they are incurred a $2000 fixed ordering cost. Use this information to answer the following questions

a: What is the optimal order quantity that the distributor should order when they order?

b: How often should the distributor place an order for this quantity?

c: If the distributor follows this ordering policy, what is the total weekly cost of the distributor? Suppose that the distributor makes a mistake, and order 1% more than the optimal policy. What is the percentage difference in cost as a result of ordering 1% more than required?

PART B: Now suppose that the distributor is able to sell each bottle for $35 per bottle. The cost per bottle is the same, namely $25 per bottle. Assume now, however, that demand is random, and that it follows a normal distribution. Use this information to answer the questions below.

a: Assume the average weekly demand is = 10000. Find the optimal solution for = 500, = 1000, = 5000, = 10000.

b: Let y be the set of optimal solutions, let x be the sigmas from the previous problem. Run a linear regression to find an equation for Q = a + b. What are the respective values for a and b?

c: What does this tell us about the optimal ordering policy with respect to the variation in our demand data?

PLEASE SHOW ALL WORK. Only need PART B answered.