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.
What will be an ideal response?

Answer:
If the hog farmer will take the leftovers:
CS = $2.50 - 0.23 = $2.27
CE = $0.23 - 0.12 = $0.11
SLT = = 0.9538
Z = 1.683
Q = 400 + 1.683 × 40 = 467.3

If the hog farmer won't take the leftovers:
CS = $2.50 - 0.23 = $2.27
CE = $0.23 - 0 = $0.23
SLT = = 0.908
Z = 1.33
Q = 400 + 1.33 × 40 = 453.1

The discrepancy, about 14 servings, shows that the barbecue joint can't be as aggressive in their production of potato salad each morning. In the new scenario, leftover potato salad is just thrown away, costing the restaurant 23 cents per serving.