A retailer is planning for the holiday season and must decide how many units of a popular gift item to order from the supplier. Demand for the…
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The retailer’s margin per unit sold is $50. Its cost of carrying unsold inventory till the end of the season is $10 per unit (e.g., if it orders 200,000 units and the actual demand is 10,000 units, then the unsold inventory is 190,000 and it costs $1.9 Million to carry it till end of the season). The retailer can return any unsold items at the end of the season at the cost at which they were purchased from the supplier. The supplier’s cost of producing the item is $80 per unit.
a. Suppose the retailer had to decide between ordering 200,000, 500,000 and 800,000 units of this gift item, which of these order quantities will maximize its expected profits?
b. How would your answer change if the retailer could not return unsold inventory at cost, but had to sell it at a loss of $80 per unit?