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 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

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?

3.  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 1 y: number of hours of assembly time at plant 2 Minimize total Star model units total Prostar model units

4.  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 1 y: number of hours of assembly time at plant 2 Minimize total Star model units total Prostar model units

5.  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 1 y: number of hours of assembly time at plant 2 Minimize total Star model units total Prostar model units

6.  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 1 y: number of hours of assembly time at plant 2 Minimize total Star model units total Prostar model units

7.  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 1 y: number of hours of assembly time at plant 2 Minimize total Star model units total Prostar model units

8.  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 1 y: number of hours of assembly time at plant 2 Minimize total Star model units total Prostar model units

9.  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 1 y: number of hours of assembly time at plant 2 Minimize total Star model units total Prostar model units

10.  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 1 y: number of hours of assembly time at plant 2 Minimize total Prostar model units

11.  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 1 y: number of hours of assembly time at plant 2 Minimize

12.  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 1 y: number of hours of assembly time at plant 2 Minimize

13.  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 1 y: number of hours of assembly time at plant 2 Minimize

14.  2009 PBLPathways Minimize

15.  2009 PBLPathways Minimize

16.  2009 PBLPathways Minimize

17.  2009 PBLPathways Minimize (90, 0) (0, 50) (40, 10)

18.  2009 PBLPathways Minimize (90, 0) (0, 50) (40, 10) (x, y)C = 2000x + 3000y (0, 50) 2000(0) + 3000(50) or 150,000 (90, 0) 2000(90) + 3000(0) or 180,000 (40, 10) 2000(40) + 3000(10) or 110,000

19.  2009 PBLPathways Minimize (90, 0) (0, 50) (40, 10) (x, y)C = 2000x + 3000y (0, 50) 2000(0) + 3000(50) or 150,000 (90, 0) 2000(90) + 3000(0) or 180,000 (40, 10) 2000(40) + 3000(10) or 110,000

20.  2009 PBLPathways Minimize (90, 0) (0, 50) (40, 10) (x, y)C = 2000x + 3000y (0, 50) 2000(0) + 3000(50) or 150,000 (90, 0) 2000(90) + 3000(0) or 180,000 (40, 10) 2000(40) + 3000(10) or 110,000

21.  2009 PBLPathways Minimize (90, 0) (0, 50) (40, 10) (x, y)C = 2000x + 3000y (0, 50) 2000(0) + 3000(50) or 150,000 (90, 0) 2000(90) + 3000(0) or 180,000 (40, 10) 2000(40) + 3000(10) or 110,000

22.  2009 PBLPathways Minimize (90, 0) (0, 50) (40, 10) (x, y)C = 2000x + 3000y (0, 50) 2000(0) + 3000(50) or 150,000 (90, 0) 2000(90) + 3000(0) or 180,000 (40, 10) 2000(40) + 3000(10) or 110,000