Problem 4-23 (Algorithmic) EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,500 windows and ended the month with 9,500 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 is possible. February March April Sales forecast 15,500 17,000 18,500 Production capacity 15,500 13,000 19,500 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 to the next will increase total costs by $0.65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate and solve a linear programming model that will minimize the cost of changing production levels while still satisfying the monthly sales forecasts. If required, round your answers to two decimal places. If an amount is zero, enter "O". Let: F= number of windows manufactured in February M = number of windows manufactured in March A-number of windows manufactured in April Im - Increase in production level necessary during month ni Dom - decrease in production level necessary during month S = ending inventary in manth m Min is + 12 + 13 + D + D2 + D s.t. Sj - Frhruary Demand (2) S! 5: 52 - March Demand (3) S2 + + A- 11 + D = (5) M- F. D = April Demand Change in February Production Change in March Production Change in April Production February Production Capacity (6) M 03 - (7) FS March Production Capacity April Production Capacity AS (9) (10) (11) (12) Sz 3 Frhruary Storage Capacity March Storage Capacity April Storage Capacity S3 S If required, round your answers to the nearest dollar Cost: 5 6,775 If required, round your answers to the nearest dollar. Cost: $ 6,775 If required, round your answers to the nearest whole number. If an amount is zero, enter "0" February March April Production Level 12,000 13,000 16,500 Increase in Production 0 1,000 3,500 Decrease in Production 3,500 0 0 Ending Inventory 6,000 2,000 0