1. Company X can purchase a certain component from either Supplier A or Supplier B. Supplier A offers an incremental quantity discount, while Supplier B offers an all-unit quantity discount.
To be specific, Supplier A charges $10 per unit for the first 3,000 units in an order, $9 per unit for the next 3,000 units in the order, and $8 per unit for any unit beyond. Supplier B charges $9 per unit for orders of no more than 8,000 units and $8.5 per unit for any bigger orders.
(a) Suppose Company X decides to buy 10,000 units from Supplier A. What is the average unit cost of the order?Please provide at least one step of calculation and the correct answer for full credit. (4 points)
(b) If Company X wants to place an order of 20,000 units, which supplier offers a lower total cost. Please provide at least one step of calculation and the correct answer for full credit. (4 points)
2. Given the following information, compute the optimal order quantities as required.
|Annual Demand||100,000 units|
|Order Cost||$200 per order|
|Inventory Holding||10% of unit cost|
(a) Suppose the unit cost of the product is $500. What is the Economic Order Quantity of the inventory control system? (You can either round up or round down.) Please include the formula, at least one step of calculation, and the correct answer for full credit. (6 points)
(b) What is the annual total cost if the Economic Order Quantity is ordered each time? Please include the formula, at least one step of calculation, and the correct answer for full credit. (6 points)
(c) Suppose an all-unit quantity discount is applied to the product. The seller charges $500 per unit for orders of no more than 1000 units and $480 per unit for any bigger orders. What is the optimal order quantity under the all-unit quantity discount? Please first calculate the EOQs for each discount price, choose the optimal order quantity for each discount price, and determine the order quantity that minimizes the total cost. (14 points)
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