Morning Star, a seller has 5 stores. Consider a new product A to be released by morning star. Demand for A at each store is independent. It is also distributed normally. The mean is 1000 units and standard deviation is 200 units. The stores have operated independently and replenishment decisions are made by the store managers. Each product costs $80 and is priced to sell at $200. Morning Star estimates that whatever inventory that is leftover can be cleared for an average price of $35 in a sale afterwards.

PART A)

1) Find the optimal order quantity,

2) the average total cost

3) average total profit at every store.

4) After that calculate the average total overall profit generated through the sale of the product for Morning Star

PART B)

Lets say that Morning Star is contemplating on only selling Product A on their online store Then, Product A will not be available at any of the retail stores. Replenishment of Product A is then made centrally and customer orders will be filled through a single central warehouse. Morning Star estimates that the demand in this case as the sum of all the demands for Product A if it were to be sold at the 5 stores. The unit cost of the product A is $80 as before. The Company will be selling the product A for $195 online. In addition, there will be an average of $2.5 shipping cost paid by Product A for the online orders. Now a wholesaler has agreed to buy all the end of season leftover inventory of Product A for the same price as part (a) ($35 per unit. No shipping or any other costs are involved in this.

Find the optimal order quantity and the average total Profit associated in this case.