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 s.t.February Demand 9000+F−s1=15000 March Demand s1+M−s2=16500 April Demand s2+A−s3=20000 Change in February Production Change in March Production F−I1+D2=0 wrong Change in April Production February Production Capacity F≤14000 March Production Capacity M≤14000 April Production Capacity A≤18000 February Storage Capacity $$F≤6000 wrong Check which variable(s) should be in your answer.March Storage Capacity $$M≤6000 wrong Check which variable(s) should be in your answer.April Storage Capacity $$A≤6000 wrong 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 = $
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 s.t.February Demand 9000+F−s1=15000 March Demand s1+M−s2=16500 April Demand s2+A−s3=20000 Change in February Production Change in March Production F−I1+D2=0 wrong Change in April Production February Production Capacity F≤14000 March Production Capacity M≤14000 April Production Capacity A≤18000 February Storage Capacity $$F≤6000 wrong Check which variable(s) should be in your answer.March Storage Capacity $$M≤6000 wrong Check which variable(s) should be in your answer.April Storage Capacity $$A≤6000 wrong 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 = $
Chapter19: Pricing Concepts
Section: Chapter Questions
Problem 6DRQ
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Question
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 |
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
s.t.February Demand
March Demand
April Demand
Change in February Production
Change in March Production
Change in April Production
February Production Capacity
March Production Capacity
April Production Capacity
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.
9000+F−s1=15000
s1+M−s2=16500
s2+A−s3=20000
F−I1+D2=0 wrong
F≤14000
M≤14000
A≤18000
$$F≤6000 wrong
Check which variable(s) should be in your answer.March Storage Capacity
$$M≤6000 wrong
Check which variable(s) should be in your answer.April Storage Capacity
$$A≤6000 wrong
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 = $
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