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A linear programming computer package is needed. E2-Windows, Incy manufactures replacement windaws 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 capscities, and the storage capabiities as shown, the management team does not think a smooth production schedule with the same production quantity each month possible. 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 esch unit increase in the production level. In addition, decreasing production by one unit from one month to the neat will increase total costs by $0,65 for each unit decrease in the production level. Ignoring production and inventory carrving costs, formulate a linear programming model that will minimize the cost (in dollars) of changing production levels while stili satisfying the monthly soles forecasts. (Let F= number of windows manufactured in Febraary, M= number of windows manufactured in March, A = number of windons manufactured in April, I1= increase in preduction level necessary during month 1,I2= increase in production level necessary during month 2,I3= increase in production level necessary during month 3,D1= decrease in productian level necessary during month 1,D2= decrease in production level necessary during month 2,D1= decrease in production level necessary during month 3,s1= ending inventory in month 1,s2= ending inventory in menth 2 , and s3= ending inventory in month 3 .) February Demand March Demand April Demand Change in February Production Change in March Production Chenge in April Preduction February Production Capsoly March Sreduction Capedty Apra Production Capacity Fecruary storage Capacty March storage Capacay A prit Storage Clapecity Find the optimal wolution. (F,N1,A1f1,f2,f2,D3D2,D3,S1,S2S1)=(Cost=1