Reddy & Rao (R& R) is a small company in India that makes handmade artistic chairs for commercial businesses. The company makes four models. The time required to make each of the models and cost per chair is given below.

R& R employs four people. Each of them works 8 hour shifts, 5 days a week (assume 4 weeks/ month). The demand for the next 3 months is estimated to be:

R& R keeps at most two of each model in inventory each month but wants to have at least one of Model D in inventory at all times. The current inventory of each model is 2. The cost to hold these finished chairs is 10% of the production cost. Develop and solve an optimization model to determine the optimal number of chairs to produce each month and the monthly inventories to minimize total cost and meet the expected demand.

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Model A Model B Model C Model D Cost per Unit $900.00 $650.00 $500.00 $750.00 Hours Required 40 per unit 12 34 Demand (Units) Model A Model B Model C Model D Month 1 Month 2 Month 3 7 4 7 4 8 5 6