example 5 Transportation
Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300
Chapter 7.2

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x Total Volume z

30,000
25 x Total Weight z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x Total Volume z

30,000
25 x Total Weight z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000 , how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x Total Volume z

30,000
25 x Total Weight z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000 , how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x Total Volume z

30,000
25 x Total Weight z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x Total Volume z

30,000
25 x Total Weight z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x

22 y

30 z

30,000
25 x Total Weight z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x

22 y

30 z

30,000
25 x Total Weight z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x

22 y

30 z

30,000
25 x

38 y

70 z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x

22 y

30 z

30,000
25 x

38 y

70 z

62,000
150 x

Total Value z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300 x : Number of units of product A y : Number of units of product B z : Number of units of product C
25 x

22 y

30 z

30,000
25 x

38 y

70 z

62,000
150 x

180 y

300 z

276,000

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300


25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




25 x

22 y

30 z

30,000
25 x

38 y

70 z

62,000
150 x

180 y

300 z

276,000

2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2

R2
-150 R1 + R3

R3

2 2

4 6
2

3 1

1
0

1

3 5



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2

R2
-150 R1 + R3

R3

2 2

4 6
2

3 1

1
0

1

3 5



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2

R2
-150 R1 + R3

R3

2 2

4 6
2

3 1

1
0

1

3 5



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2

R2
-150 R1 + R3

R3

2 2

4 6
2

3 1

1
0

1

3 5



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2
-150 R1 + R3


R2
R3

25

22

30

30,000
25 38 70 62,000
0 16 40 32,000



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2
-150 R1 + R3


R2
R3

25

22

30

30,000
25 38 70 62,000
0 16 40 32,000



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2
-150 R1 + R3


R2
R3

150

132

180

180,000
150 180 300 276,000
0 48 120 96,000



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2
-150 R1 + R3


R2
R3

150

132

180

180,000
150 180 300 276,000
0 48 120 96,000



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways



25 22 30 30,000


25 38 70 62,000
150 180 300 276,000




1
25
R1

R1


1 22
25
6
5
1, 200


25 38 70 62,000
150 180 300 276,000




-25 R1 + R2
-150 R1 + R3


R2
R3

150

132

180

180,000
150 180 300 276,000
0 48 120 96,000



1 22
25
0 16
6
5
40
1, 200
32,000
0 48 120 96,000





2009 PBLPathways





1 22
25
6
5
1, 200
0 16 40 32,000
0 48 120 96,000




1
16
R2

R2



1
0
22
25
1
6
5
5
2
1, 200
2,000
0 48 120 96,000





22
25
R2 + R1

R1
-48 R2 + R3

R3

2 2

4 6
2

3 1

1
0

1

3 5




1 0

1

560
0 1 5
2
0 0 0
2,000
0





2009 PBLPathways





1 22
25
6
5
1, 200
0 16 40 32,000
0 48 120 96,000




1
16
R2

R2



1
0
22
25
1
6
5
5
2
1, 200
2,000
0 48 120 96,000





22
25
R2 + R1

R1
-48 R2 + R3

R3

2 2

4 6
2

3 1

1
0

1

3 5




1 0

1

560
0 1 5
2
0 0 0
2,000
0





2009 PBLPathways





1 22
25
6
5
1, 200
0 16 40 32,000
0 48 120 96,000




1
16
R2

R2



1
0
22
25
1
6
5
5
2
1, 200
2,000
0 48 120 96,000





22
25
R2 + R1

R1
-48 R2 + R3

R3

2 2

4 6
2

3 1

1
0

1

3 5




1 0

1

560
0 1 5
2
0 0 0
2,000
0





2009 PBLPathways





1 22
25
6
5
1, 200
0 16 40 32,000
0 48 120 96,000




1
16
R2

R2



1
0
22
25
1
6
5
5
2
1, 200
2,000
0 48 120 96,000





22
25
R2 + R1

R1
-48 R2 + R3

R3
0
1

22

25
11
5
22
25
1 0

1,760
6 1, 200
5

1

560




1 0

1

560
0 1 5
2
0 0 0
2,000
0





2009 PBLPathways





1 22
25
6
5
1, 200
0 16 40 32,000
0 48 120 96,000




1
16
R2

R2



1
0
22
25
1
6
5
5
2
1, 200
2,000
0 48 120 96,000





22
25
R2 + R1

R1
-48 R2 + R3

R3
0
1

22

25
11
5
22
25
1 0

1,760
6 1, 200
5

1

560




1 0

1

560
0 1 5
2
0 0 0
2,000
0





2009 PBLPathways





1 22
25
6
5
1, 200
0 16 40 32,000
0 48 120 96,000




1
16
R2

R2



1
0
22
25
1
6
5
5
2
1, 200
2,000
0 48 120 96,000





22
25
R2 + R1

R1
-48 R2 + R3

R3
0

48

120

96,000
0 48 120 96,000
0 0 0 0




1 0

1

560
0 1 5
2
0 0 0
2,000
0





2009 PBLPathways





1 22
25
6
5
1, 200
0 16 40 32,000
0 48 120 96,000




1
16
R2

R2



1
0
22
25
1
6
5
5
2
1, 200
2,000
0 48 120 96,000





22
25
R2 + R1

R1
-48 R2 + R3

R3
0

48

120

96,000
0 48 120 96,000
0 0 0 0




1 0

1

560
0 1 5
2
0 0 0
2,000
0





2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300




1 0

1

560
0
0
1
0
5
2
0
2,000
0



 x
 z
 
560 y

5
2 z

2000 x y
 

560

2000
 z
5
2 z

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300




1 0

1

560
0
0
1
0
5
2
0
2,000
0



 x
 z
 
560 y

5
2 z

2000 x y
 

560

2000
 z
5
2 z

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300




1 0

1

560
0
0
1
0
5
2
0
2,000
0



 x
 z
 
560 y

5
2 z

2000 x y
 

560

2000
 z
5
2 z

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300
All variables must be nonnegative x
 
560
 z y

2000

5
2 z

560 z
2000

5

2 z
0
0 z

560 z

800

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300
All variables must be nonnegative x
 
560
 z y

2000

5
2 z

560 z
2000

5

2 z
0
0 z

560 z

800

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300
All variables must be nonnegative x
 
560
 z y

2000

5
2 z

560 z
2000

5

2 z
0
0
560 800

2009 PBLPathways

Ace Trucking Company has an order for three products, A, B, and C, for delivery. The table below gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Product A Product B Product C
Unit Volume
(cubic feet)
Weight (pounds)
Value (dollars)
25
25
150
22
38
180
30
70
300
Units of Product C carried:
Units of Product A carried:
Units of Product B carried:
560 800 x
 
560
 z y

2000

5
2 z and z is an even integer

2009 PBLPathways