EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 10,000 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 is possible.

EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 10,000 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 is possible.

	February	March	April
Sales forecast	15,000	15,500	20,500
Production capacity	13,000	15,000	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

I_m = increase in production level necessary during month m

D_m = decrease in production level necessary during month m

s_m = ending inventory in month m

Min	I1 + I2 + I3 + D1 + D2 + D3
s.t.
(1)	F - s1 =	February Demand
(2)	s1 + M - s2 =	March Demand
(3)	s2 + A - s3 =	April Demand
(4)	F - I1 + D1 =	Change in February Production
(5)	M - F - I2 + D2 =	Change in March Production
(6)	A - M - I3 + D3 =	Change in April Production
(7)	F	February Production Capacity
(8)	M	March Production Capacity
(9)	A	April Production Capacity
(10)	s1	February Storage Capacity
(11)	s2	March Storage Capacity
(12)	s3	April Storage Capacity

If required, round your answers to the nearest dollar.

Cost: $

If required, round your answers to the nearest whole number. If an amount is zero, enter "0"

	February	March	April
Production Level
Increase in Production
Decrease in Production
Ending Inventory

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

I_m = increase in production level necessary during month m

D_m = decrease in production level necessary during month m

s_m = ending inventory in month m