A linear programming computer package is needed.

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.

FebruaryMarchAprilSales forecast15,00016,50020,000Production capacity14,00014,00018,000Storage capacity6,0006,0006,000

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 a linear programming model that will minimize the cost (in dollars) 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, I₁ = increase in production 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 production level necessary during month 1, D₂ = decrease in production level necessary during month 2, D₃ = decrease in production level necessary during month 3, s₁ = ending inventory in month 1, s₂ = ending inventory in month 2, and s₃ = ending inventory in month 3.)

Min

s.t.February Demand

Check how many equations are needed.March Demand

Check how many equations are needed.April Demand

Check how many equations are needed.Change in February Production

FI1+D1=15,000

Change in March Production

MFI2+D2=0

Change in April Production

AMI3+D3=0

February Production Capacity

F14,000

March Production Capacity

M14,000

April Production Capacity

A18,000

February Storage Capacity

Check which variable(s) should be in your answer.March Storage Capacity

Check which variable(s) should be in your answer.April Storage Capacity

Check which variable(s) should be in your answer.

Find the optimal solution.

(F, M, A, I₁, I₂, I₃, D₁, D₂, D₃, s₁, s₂, s₃) =

Cost = $