ewline\"> The PUPR has given Vecino’s Bakery the concession to sell glazed donut

Question

ewline"> The PUPR has given Vecino’s Bakery the concession to sell glazed donuts at the Graduate School during evening classes. It costs the bakery $.15 to produce each donut, and Vecino’s sells the donuts to students for $0.35 each. Any donuts that are unsold at the end of the evening are donated to a local charity, and the bakery obtains a tax credit equal to $.05 per donut. If Vecino’s produces too few donuts and does not have enough to satisfy all its customers, it incurs a customer goodwill cost of $.25 per donut demanded. The bakery hires a student to operate the concession and pays the student $15 per evening. After several months of operations, the bakery has determined that demand for glazed donuts on weekday evenings approximately follows a normal distribution with a mean of 120 and a standard deviation of 20. Vecino’s wishes to determine the optimal number of donuts to prepare for weekday evenings.

Explanation / Answer

Vecino should prepare 129 donouts

Mean (µ) = 120 SD () = 20 Cost of Ticket = 80 Cost of underage (shortage) (Cu) = 0.2 =0.35-0.15 = Cost of shortage of one unit less than actual demand (shortage of inventory) Cost of overage (excess) (Co) = 0.1 =0.15-0.05 =Cost of excess of one unit (leftover inventory) Critical Ratio or P(D<=Q) = Cu Cu + Co P(D<=Q) = 0.6667 Look corresponding Z score from standard normal table for critical ratio as cum probability z = 0.4307 Q = z + µ Q = 129

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