Lowland Appliance replenishes its stock of 52-inch flat-screen TVs three times a year. Each order takes 1/9 of a year to arrive. Annual demand for these TVs follows a normal distribution with a mean of 990 and a standard deviation of 40. Assume that the cost of holding a TV in inventory for a year is $100. Assume that Lowland begins with 500 of these TVs in inventory, the cost of a shortage is $150, and the cost of placing an order is $500.

a. Suppose that whenever inventory is reviewed, and the inventory level is I, an order for 480I of these TVs is placed. Use simulation to estimate the average annual cost of this policy. Such a policy is called an order-up policy.

b. Use simulation to estimate the average annual cost for order-up policies when Lowland orders up to 200, 400, 600, and 800 of these TVs.