Problem 3 12. Grafton Metalworks Company produces metal alloys from six different ores it mines. The com- pany 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 cach ore are provided in the following table: Metal (%) A BCD Impurities (%) Ore Cost/Ton 19 15 12 14 40 $27 43 10 25 15 25 3. 17 53 30 32 20 12 18 50 22 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 cach 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.

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ISBN:9781337406659
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Publisher:WINSTON, Wayne L.
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Problem 3
12. Grafton Metalworks Company produces metal alloys from six different ores it mines. The com-
pany 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 cach
of the six ores and the level of impurities in each ore are provided in the following table:
Metal (%)
A BC D
Cost/Ton
Ore
Impurities (%)
19
15
12
14
40
$27
43
10
25
15
25
3
17
53
30
32
20
12
18
50
22
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.
Transcribed Image Text:Problem 3 12. Grafton Metalworks Company produces metal alloys from six different ores it mines. The com- pany 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 cach of the six ores and the level of impurities in each ore are provided in the following table: Metal (%) A BC D Cost/Ton Ore Impurities (%) 19 15 12 14 40 $27 43 10 25 15 25 3 17 53 30 32 20 12 18 50 22 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.
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