Conceptual Overview: Explore how to find the optimal order quantity for uniform demand. A buyer for a store must decide six months in advance how many items of a seasonal product to purchase. Buying too few items will mean lost sales. Assume the lost profit from those sales Cu = $20 per item. On the other hand, buying too many will result in lower profits from the items sold at a season-ending sale. Assume those costs Cs = $10 per item. The optimal order size Q must satisfy this condition: \small P(demand \le Q^*) = \frac{C_u}{C_u + C_s} = \frac{20}{20 + 10} = \frac{20}{30} = \frac{2}{3} = 0.667

P(demandQ )= C u +C s C u = 20+10 20 = 30 20 = 3 2 =0.667 Assuming demand has a uniform distribution between the ranges of 350 and 650 items with a mean of 500 items, drag on the graph to find the optimal order quantity. For the optimal quantity, P(demand <= Q*) = 0.667 (about). 350 500 650 Demand 550

1. Suppose the loss incurred by selling an item at the season-ending sale was equal to the lost profit of a lost sale. What would the optimal order quantity be in this case?

1. 350
2. 450
3. 500
4. 600

2. Using the uniform distribution of demand, which of the following is least accurate?

1. If C[u] is 3 times as large as C[s], then the optimal order quantity is always 575.
2. If C[u] is increased while holding C[s] constant, the optimal order quantity will increase.
3. If C[s] is increased while holding C[u] constant, the optimal order quantity will decrease.
4. If the lost profit due to under-ordering (C[u]) is zero, then the optimal order quantity is 650.