EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 9,000 windows in inventory. EZ-Windows’ management team would like to develop a production schedule for the next three months. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a similar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown, the management team does not think a smooth production schedule with the same production quantity each month possible. February March April Sales forecast 15,000 16,500 20,000 Production capacity 14,000 14,000 18,000 Storage capacity 6,000 6,000 6,000 The company’s cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1.00 for each unit increase in the production level. In addition, decreasing production by one unit from one month the next will increase total costs by $0.65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate a linear programming model that will minimize the cost of changing production levels while still satisfying the monthly sales forecasts. (Let F = number of windows manufactured in February, M = number of windows manufactured in March, A = number of windows manufactured in April, 1= increase in production level necessary during month 1, 12 = increase in production level necessary during month 2, 13 = increase in production level necessary during month 3, D = decrease in production level necessary during month 1, D2 = decrease in production level necessary during month 2, D3 = decrease in production level necessary during mont 3, 5, = ending inventory in month 1, s2 = ending inventory in month 2, and s3 = ending inventory in month 3.) Min s.t. February Demand March Demand April Demand Change in February Production Change in March Production Change in April Production April Demand Change in February Production Change in March Production Change in April Production February Production Capacity March Production Capacity April Production Capacity February Storage Capacity March Storage Capacity April Storage Capacity Find the optimal solution. (F, M, A, 11, 12, 13, D1, D2, D3, S1, 52, 53) = 1) Cost = $