A retailer wishes to buy a seasonal product from a supplier at an offered wholesale price of $70 per unit and will sell it for $200 each. Due to some hazardous materials content, any unsold product left over at the end of the selling season has to be disposed of properly by the retailer at a cost of $5 per unit. The supplier’s manufacturing and shipping costs for this item amount to $40 per unit. The retail demand during the selling season for this item is uncertain, but can be expressed by the following probability distribution: Demand (units): 0 1 2 3 4 5 6 7 8
Probability: 0.05 0.1 0.15 0.15 0.2 0.1 0.1 0.1 0.05
(a) How many of units of this product should be ordered by the retailer. What are the resulting retailer’s expected profit and the supplier’s profit?
(b) The supplier has made an offer to the retailer such that the wholesale price would be reduced to $40 per unit, with the provision that the former will receive 20% of all revenues generated by the retail sales of this item. What are the retailer’s and supplier’s expected profits now. Consequently, should the retailer accept this offer from the supplier? Does the supplier have anything to gain from this proposed arrangement?