Champion Electronics Warehouse sells a certain brand of headsets that it orders from Reliance Electronics in Japan. The probability distribution of demand per week for the headsets and the probability distribution of the replenishment lead time for the headset orders placed, which were developed from past records, are as shown in the following tables. Champion would like to establish an inventory policy of ordering 20 headsets whenever the inventory level drops to 5 units. The replenishment lead time that varies by 1, 2, 3, or 4 weeks means that if the replenishment lead time is 2 weeks, an order placed on week 1 will arrive at the beginning of week 4. Any unmet customer demand for headsets as a result of inventory shortage will be lost with a lost sales cost of $200. The costs associated with ordering headsets and holding inventory are $70 per order and $20 per headset per week. Assuming a beginning inventory of 8 headsets, conduct a 10-week Monte Carlo simulation experiment and compute total inventory costs for this simulation study:

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Weekly Demand 10 0.02 0.08 0.12 0.25 0.05 0.05 0.03 0.05 0.20 0.15 Probability Lead Time per Week 1 4 Probability 0.20 0.30 0.40 0.10