### Determine the optimal number of donuts to prepare

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The university has given Vecino’s Bakery the concession to sell glazed donuts in the Graduate School of Business Administration 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.

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