Problem 4-23 (Algorithmic) EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 9,500 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 15,000 17,000 20,000 Production capacity 14,000 15,500 17,000 Storage capacity 6,000 6,000 6,000 The companys 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 "0". 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 m Dm = decrease in production level necessary during month m sm = ending inventory in month m Min fill in the blank 1 1 I1 + fill in the blank 2 1 I2 + fill in the blank 3 1 I3 + fill in the blank 4 0.65 D1 + fill in the blank 5 0.65 D2 + fill in the blank 6 0.65 D3 s.t. (1) fill in the blank 7 1 F - fill in the blank 8 s1 = fill in the blank 9 6,000 February Demand (2) fill in the blank 10 s1 + fill in the blank 11 M - fill in the blank 12 s2 = fill in the blank 13 16,500 March Demand (3) fill in the blank 14 s2 + fill in the blank 15 A - fill in the blank 16 s3 = fill in the blank 17 20,000 April Demand (4) fill in the blank 18 F - fill in the blank 19 I1 + fill in the blank 20 D1 = fill in the blank 21 15,000 Change in February Production (5) fill in the blank 22 M - fill in the blank 23 F - fill in the blank 24 I2 + fill in the blank 25 D2 = fill in the blank 26 0 Change in March Production (6) fill in the blank 27 A - fill in the blank 28 M - fill in the blank 29 I3 + fill in the blank 30 D3 = fill in the blank 31 0 Change in April Production (7) fill in the blank 32 F fill in the blank 33 14,000 February Production Capacity (8) fill in the blank 34 M fill in the blank 35 14,000 March Production Capacity (9) fill in the blank 36 A fill in the blank 37 18,000 April Production Capacity (10) fill in the blank 38 s1 fill in the blank 39 6,000 February Storage Capacity (11) fill in the blank 40 s2 fill in the blank 41 6,000 March Storage Capacity (12) fill in the blank 42 s3 fill in the blank 43 6,000 April Storage Capacity If required, round your answers to the nearest dollar. Cost: $ fill in the blank 44 6,450 If required, round your answers to the nearest whole number. If an amount is zero, enter "0" February March April Production Level fill in the blank 45 12,000 fill in the blank 46 1,400 fill in the blank 47 16,500 Increase in Production fill in the blank 48 0 fill in the blank 49 2,000 fill in the blank 50 2,500 Decrease in Production fill in the blank 51 3,000 fill in the blank 52 0 fill in the blank 53 0 Ending Inventory fill in the blank 54 6,000 fill in the blank 55 3,500 fill in the blank 56 0 Feedback Partially correct Check My Work