RistoranteDiRoma offers two types of pizza (cheese or pepperoni) in its menu. Since, the restaurant does not specialize in pizza, the pizzas are ordered from another prepared food store. Luigi, the owner of the restaurant, estimates that the monthly demand for the cheese pizza is normal with a mean of 150 and standard deviation of 30. Similarly, monthly demand for pepperoni is also normal with mean 180 and standard deviation 40. It costs $50 to place an order at the supplier (food store) and takes 5 days for the order to arrive at the restaurant. Cheese and pepperoni pizza costs $6 and $8, respectively. Assume that the annual interest rate is 12%. Luigi sets the maximum chance of stockout to 10% not to upset his customers and estimates that it costs $15 per pizza short including the loss of goodwill. (Assume 30 days/month).

a) Determine the economic order quantity (EOQ), reorder point (R), and the average number of shortages per month for each type of pizza. Also find the average monthly total cost for this system.

b) Luigi claims that it would help reduce the cost to order only the pizza dough from the prepared food store. He claims they could add the toppings when the demand is realized (when a customer orders a pizza) at an additional cost of $2. It costs $3.5 for a pizza dough and ordering cost remains the same at $50 per order. The delivery times will remain as before. Find the average and standard deviation of the monthly demand for the pizza dough. Also determine the economic order quantity (EOQ) and the reorder point (R) for the pizza dough.

c) Find the average cost associated with this alternative. Do you think Luigi should take this action?