Question 4: Newsvendor Model (20 points)

Ankara-Dner prepares very delicious dner sandwiches. Meat for the dner sandviches is bought from a supplier named MS with a price of $4 per kg. 10 dner sandwiches can be prepared from each kilogram of meat. Any leftover meat is disposed to garbage center with a cost of $1 per kg. Dner sandwiches sell for $3 each. All other inputs other than the meat (e.g., labor, other ingredients like turu, salad, etc.) cost $0.6 per each dner sandwich sold. Demand for meat is normally distributed with a mean of 800 kg per week and a standard deviation of 200 kg. per week. (Note: The standard normal distribution table and the mismatch table are provided in the formula sheet.)

a) (10 points) How many kg of meat should Ankara-Dner order per week from MS if the objective is to maximize the expected profit per week?

b) (5 points) What will be Ankara-Dners expected profit per week based on the above ordering quantity?

c) (5 points)Find the new mismatch cost if new order quantity Q becomes 1060 kg per week (assuming that values other than order quantity and z value remains same).