During the week of the Passover holiday, Jews all over the world eat a special type of bread called matzah .1 The small Jewish community in San Jose, Costa Rica, consists of approximately 1,000 families. There is only one Jewish restaurant in San Jose that is supplying matzah bread to the entire Jewish community during the week of Passover at a price of $20 per box of matzah bread. To meet its demand during the week of Passover, the restaurant orders the matzah bread from a Mexican supplier about two months before the holiday . The Mexican supplier charges a wholesale price of $11 for one box of matzah bread . The cost to manufacture each box is $4, and the restaurant incurs an additional transportation cost of $1 for each box it orders. The owner of the restaurant estimates that the level of demand for matzah bread during the week of Passover will be normally distributed with a mean of 6000, and a standard deviation of 1581.
The demand for matzah bread at the end of the week is close to zero, and thus it has no salvage value for the San Jose restaurant.
1. How many boxes of matzah bread should the restaurant order from its Mexican supplier? What would the restaurant ‘s profit from that order be?
2. What is the Mexican supplier’s profit from the Costa Rican market? What are the total supply chain profits?
3. Suppose that the restaurant owner and the Mexican supplier were working together to maximize the entire chain’s profits, what would be the optimal ordering quantity of boxes of matzah for the entire supply chain? What would be the total supply chain profits? What is the supply chain loss (the loss in profit because the supply chain is not coordinated)?
4. A plan under discussion is for the supplier to pay the restaurant $7 for any unsold inventory? Under this plan how many boxes of matzah bread should the restaurant order? What is the expected profit for the restaurant? What is the expected profit for the supplier? What should the supplier do?
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