Problem 1. XYZ company would like to pursue the optimal quantity based on the situation that a supplier of a particular raw material is offering at five different prices, depending on the size of the order.
0 < Q < = 300 pounds => $20 per pound
300 < Q < = 600 pounds => 3% discount from the original price
600 < Q < = 1000 pounds => 5% discount from the original price
1000 < Q < = 5000 pounds => 10% discount from the original price
> 5000 pounds => 15% discount from the original price
The cost of placing an order is $40. Annual demand is 3,000 pounds. Holding cost is 25 percent of the material price.
a. What replenishment size should be used? Show all possible total costs.
b. If the supplier improves the discount rate of the 600 < Q <= 1000 pounds from 5% discount to 9% discount, would the replenishment size change?
c. Continuing from part b, at what price will ordering at lot size 5000 or more be more attractive than ordering at lot size <= 5000?