a) Xelia Corporation is a supplier of control systems to major avionics companies. Demand for control systems is about 2000 units per year. The Xelia plant in Minneapolis can produce at a rate of 200 units per month. Each unit costs Xelia $100 to produce and the setup cost for beginning a production run is $1000. Assume the company uses an annual rate of return on investments of 25%. What is the optimal number of units to produce in each run? What is total cost? What is the utilization of the production facility? What is the maximum dollar investment in finished goods inventory that Xelia has at any time?

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b) Xelia decides to diversify its product portfolio by introducing 4 different versions of its control systems that will replace the current one. The company expects the total annual demand of 2000 to remain the same but to be now equally divided among the four versions. Xelia expects to charge higher prices for the newer versions. If production of these four versions is carried in a strictly cyclic fashion, what is the optimal number of units of each version Xelia should produce in each cycle? What is the new total cost? In order to justify the introduction of these new versions, what should be the minimum increase in the price of each unit? Assume production and setup costs are the same as those in question a) and equal for all products.