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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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