Question

The UPR has given Compa’s Bakery the concession to sell glazed donuts at the Graduate School during evening classes. It costs the bakery $.20 to produce each donut, and Compa’s sells the donuts to students for $0.45 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 Compa’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. Compa’s wishes to determine the optimal number of donuts to prepare for weekday evenings.

Answer 1

The cost of understocking (Cu) = (0.45-0.20) + 0.25 = 0.50

The cost of overstocking (Co) = (0.20-0.05) = 0.15

This means the critical ratio = Cu/(Cu + Co) 0.50/(0.50 + 0.15) = 0.7692

The z value = 0.7362

The optimal quantity is 120 + 0.7362*20 = 134.74 or 135 units

The optimal number of donuts is 135 units