# MAT540 Week 8 Homework Essay

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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
The cost of shipping coal from each mine to each plant, the capacity at each of the three mines and the demand at each plant are shown in the following table:

Plant Mine
1
2
3
4
Mine Capacity (tons)
1
\$ 7
\$ 9
\$10
\$12
220
2
9
7
8
12
170
3
11
14
5
7
280
Demand (tons)
110
160
90
180

The cost of mining and processing coal is \$62 per ton at mine 1, \$67 per ton at mine 2, and \$75 per ton at mine 3. The percentage of ash and sulfur content per ton of coal at each mine is as follows: Mine
% Ash
% Sulfur
1
9
6
2
5
4
3
4
3

Each plant has different cleaning equipment. Plant 1 requires that the coal it receives have no more than 6% ash and 5% sulfur; plant 2 coal can have no more than 5% ash and sulfur combined; plant 3 can have no more than 5% ash and 7% sulfur; and plant 4 can have no more than 6% ash and sulfur combined. CCC wabts to determine the amount of coal to produce at each mine and ship to its customers that will minimize its total cost. a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer. 36. Joe Henderson runs a small metal parts shop. The shop contains three machines – a drill press, a lathe, and a grinder. Joe has three operators, each certified to work on all three