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.

	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 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: I_1+I_2+I_3+0.65D_1+0.65D_2+0.65D_3

February Demand:

March Demand:

April Demand:

Change in February production:

Change in March production:

Change in April production:

February storage: s_1 6000

March Storage capacity: s_2 6000

April Storage capacity: s_3 6000

Find the optimal solution:

Cost = $