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LIMECO owns a lime factory and sells six grades of lime (grades 1 through 6). The sales price per pound is given in Table.
|
Grade |
1 |
2 |
3 |
4 |
5 |
6 |
|
Price($) |
12 |
14 |
10 |
18 |
20 |
25 |
Lime is produced by kilns. If a kiln is run for an 8-hour shift, the amounts (in pounds) of each grade of lime given in Table are produced.
|
Grade |
1 |
2 |
3 |
4 |
5 |
6 |
|
Amount produced |
2 |
3 |
1 |
1.5 |
2 |
3 |
It costs $150 to run a kiln for an 8-hour shift. Each day the factory believes it can sell up to the amounts (in pounds) of lime given in Table.
|
Grade |
1 |
2 |
3 |
4 |
5 |
6 |
|
Maximum demand |
20 |
30 |
40 |
35 |
25 |
50 |
Lime that is produced by the kiln may be reprocessed by using any one of the five processes described in Table.
|
Input (1 Lb) |
Output |
Cost ($ per Lb of Input) |
|
Grade 1 |
.3 lb Grade 3 |
 |
|
 |
.2 lb Grade 4 |
2 |
|
 |
.3 lb Grade 5 |
 |
|
 |
.2 lb Grade 6 |
 |
|
Grade 2 |
1 lb Grade 6 |
1 |
|
Grade 3 |
.8 lb Grade 4 |
1 |
|
Grade 4 |
.5 lb Grade 5 |
1 |
|
 |
.5 lb Grade 6 |
 |
|
Grade 5 |
.9 lb Grade 6 |
2 |
For example, at a cost of $1/lb, a pound of grade 4 lime may be transformed into .5 lb of grade 5 lime and .5 lb of grade 6 lime.
Any extra lime leftover at the end of each day must be disposed of, with the disposal costs (per pound) given in Table.
|
Grade |
1 |
2 |
3 |
4 |
5 |
6 |
|
Cost of Disposition ($) |
3 |
2 |
3 |
2 |
4 |
2 |
Formulate an LP whose solution will tell LIMECO how to maximize their daily profit.
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