MAT540 Week 8 Homework
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MAT540 Week 8 Homework
Chapter 4
14. Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 21% of metal A, no more than 12% of metal B, no more than 7% of metal C and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table:
Ore
Metal (%)
Impurities (%)
Cost/Ton
A
B
C
D
1
19
15
12
14
40
27
2
43
10
25
7
15
25
3
17
0
0
53
30
32
4
20
12
0
18
50
22
5
0
24
10
31
35
20
6
12
18
16
25
29
24
When the metals are processed and refined, the impurities are removed.
The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer. 19. As a result of a recently passed bill, a congressman’s district has been allocated $4 million for programs and projects. It is up to the congressman to decide how to distribute the money. The congressman has decided to allocate the money to four ongoing programs because of their importance to his district – a job training program, a parks project, a sanitation project, and a mobile library. However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election. His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows. Program
Votes/ Dollar
Job training
0.02
Parks
0.09
Sanitation
0.06
Mobile library
0.04
In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following
MAT540 Week 8 Homework
Chapter 4
14. Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 21% of metal A, no more than 12% of metal B, no more than 7% of metal C and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table:
Ore
Metal (%)
Impurities (%)
Cost/Ton
A
B
C
D
1
19
15
12
14
40
27
2
43
10
25
7
15
25
3
17
0
0
53
30
32
4
20
12
0
18
50
22
5
0
24
10
31
35
20
6
12
18
16
25
29
24
When the metals are processed and refined, the impurities are removed.
The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer. 19. As a result of a recently passed bill, a congressman’s district has been allocated $4 million for programs and projects. It is up to the congressman to decide how to distribute the money. The congressman has decided to allocate the money to four ongoing programs because of their importance to his district – a job training program, a parks project, a sanitation project, and a mobile library. However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election. His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows. Program
Votes/ Dollar
Job training
0.02
Parks
0.09
Sanitation
0.06
Mobile library
0.04
In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following