Joe's Coffee Shop has fresh muffins delivered each morning. Daily demand for muffins is approximately normal with a mean of 2000 and a standard deviation of 150. Joe pays $0.40 per muffin and sells each muffin for $1.25. Joe and the staff eat any leftovers they can and throw the rest, instead of feeding homeless. What a shame! a) Find the optimal order quantity for Joe that minimizes his cost. Does the number make any sense? Why or why not? b) Using simulation, create random demand numbers and find the expected profit from the muffins if Joe orders the optimal order quantity. Try two other order quantities to illustrate the change in the expected profit. Provide a short discussion on the relevance of the optimal order quantity and the mean demand.

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