Example $12-1$: Evaluating the optimal service level for seasonal items

The manager at Sportmart, a sporting goods store, has to decide on the number of skis to purchase for the winter season. Based on past demand data and weather forecasts for the year, management has forecast demand to be normally distributed, with a mean of

M $=350$ and a standard deviation of o $=100.$ Each pair of skis costs c $=$ $$100$ and retails

for p $=$ $$250.$ Any unsold skis at the end of the season are disposed of for $$85.$ Assume

that it costs $$5$ to hold a pair of skis in inventory for the season. How many skis should the manager order to maximize expected profits?