A Local Barbecue Joint Makes One Massive Batch of Potato

Essay

A local barbecue joint makes one massive batch of potato salad each day. If they run out of this savory side before the end of the day, their last few customers are less than satisfied, but if they make too much, they sell it to the local hog farmer for feed. Every serving costs an equivalent of $0.23 to make, but can be sold for $2.50 to customers and for $0.12 to the hog farmer. The average daily demand is for 400 servings with a standard deviation of 40 servings. How many servings should be made each day? One day the hog farmer cancels the contract - evidently there are some things that even hogs won't eat. With no fallback position, how many servings of potato salad should the barbecue joint make? Discuss the discrepancy between the two numbers.