PROMISE I WILL LIKE... all three please

1. The inventory for an item in a company grows gradually. The item arrives at the rate of 20 units per week and is used with the rate of 5 units per week. The item costs $2,000 per unit. The setup / ordering cost is $10,000 and the annual holding cost is 25 percent of the cost.

1. Which one the following models should be used: EOQ (Economic Order Quantity) model or POQ (Production Order Quantity) model? Why?
2. What is the optimal lot size?
3. What is the annual setup cost of the optimal policy?
4. What is the annual holding cost?

2. Demand for an item is 20,000 boxes per month. The holding cost is 20 percent per year. Each order incurs a fixed cost of $400. The supplier offers an all unit discount pricing scheme with a price of $5 per box for orders under 30,000 and a price of $4.90 for all orders of 30,000 or more. How many boxes should be ordered per replenishment?

3. The Blue company has introduced a new music device called Juke. The production cost for Blue is $100 per Juke. Juke is sold through Buy-Buy, a major electronics retailer. Buy-Buy has estimated that demand for Juke will depend on the final retail price p according to the demand curve

Demand D=2,000,0002,000 p

1. What wholesale price should Blue charge for Juke? At this wholesale price, what retail price should Buy-Buy set? What are the profits for Blue and Buy-Buy at equilibrium?
2. If Blue decides to discount the wholesale price by $40, how much of a discount should Buy-Buy offer to customers if it wants to maximize its own profits? What fraction of the discount offered by Blue does Buy-Buy pass along to the customer?