example 2 cost minimization chapter 8.2 star manufacturing company produces two types of dvd...
TRANSCRIPT
![Page 1: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/1.jpg)
example 2 Cost Minimization
Chapter 8.2
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
2009 PBLPathways
![Page 2: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/2.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
![Page 3: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/3.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Star model units
total Prostar model units
![Page 4: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/4.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Star model units
total Prostar model units
![Page 5: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/5.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Star model units
total Prostar model units
![Page 6: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/6.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Star model units
total Prostar model units
![Page 7: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/7.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Star model units
total Prostar model units
![Page 8: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/8.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Star model units
total Prostar model units
![Page 9: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/9.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Star model units
total Prostar model units
![Page 10: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/10.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
total Prostar model units
![Page 11: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/11.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
![Page 12: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/12.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
![Page 13: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/13.jpg)
2009 PBLPathways
Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant 1 can assemble 60 units of the Star model and 80 units of the Prostar model per hour, and plant 2 can assemble 300 units of the Star model and 80 units of the Prostar model per hour. The company needs to produce at least 5400 units of the Star model and 4000 units of the Prostar model to fill an order. If it costs $2000 per hour to run plant 1 and $3000 per hour to run plant 2, how many hours should each plant spend on manufacturing DVD players to minimize its cost for this order? What is the minimum cost for this order?
x: number of hours of assembly time at plant 1y: number of hours of assembly time at plant 2
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
![Page 14: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/14.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
60 300 5400x y
80 80 4000x y
![Page 15: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/15.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
60 300 5400x y
80 80 4000x y
![Page 16: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/16.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
60 300 5400x y
80 80 4000x y
![Page 17: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/17.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
(90, 0)
(0, 50)
(40, 10)
![Page 18: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/18.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
(90, 0)
(0, 50)
(40, 10)
(x, y) C = 2000x + 3000y
(0, 50)2000(0) + 3000(50)
or150,000
(90, 0)2000(90) + 3000(0)
or180,000
(40, 10)2000(40) + 3000(10)
or110,000
![Page 19: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/19.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
(90, 0)
(0, 50)
(40, 10)
(x, y) C = 2000x + 3000y
(0, 50)2000(0) + 3000(50)
or150,000
(90, 0)2000(90) + 3000(0)
or180,000
(40, 10)2000(40) + 3000(10)
or110,000
![Page 20: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/20.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
(90, 0)
(0, 50)
(40, 10)
(x, y) C = 2000x + 3000y
(0, 50)2000(0) + 3000(50)
or150,000
(90, 0)2000(90) + 3000(0)
or180,000
(40, 10)2000(40) + 3000(10)
or110,000
![Page 21: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/21.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
(90, 0)
(0, 50)
(40, 10)
(x, y) C = 2000x + 3000y
(0, 50)2000(0) + 3000(50)
or150,000
(90, 0)2000(90) + 3000(0)
or180,000
(40, 10)2000(40) + 3000(10)
or110,000
![Page 22: Example 2 Cost Minimization Chapter 8.2 Star Manufacturing Company produces two types of DVD players, which are assembled at two different locations. Plant](https://reader036.vdocuments.us/reader036/viewer/2022070413/5697bfa81a28abf838c99273/html5/thumbnails/22.jpg)
2009 PBLPathways
Minimize 2000 3000C x y
60 300 5400
80 80 4000
x y
x y
0, 0x y
Minimize 2000 3000C x y
18 0.2
50
y x
y x
0, 0x y
(90, 0)
(0, 50)
(40, 10)
(x, y) C = 2000x + 3000y
(0, 50)2000(0) + 3000(50)
or150,000
(90, 0)2000(90) + 3000(0)
or180,000
(40, 10)2000(40) + 3000(10)
or110,000