LIMECO owns a lime factory and sells six grades of lime (grades 1 through 6). The sales price per pound is given in Table 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 26 are produced. 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 27.
Lime that is produced by the kiln may be reprocessed by using any one of the five processes described in Table 28.
For example, at a cost of $1/lb, a pound of grade 4 lime may be transformed into .5 lb of grade 5 lime and .5 lb of grade 6 lime.
Any extra lime leftover at the end of each day must be disposed of, with the disposal costs (per pound) given in Table 29.
Formulate an LP whose solution will tell LIMECO how to maximize their daily profit.
table 25
Grade | 1 | 2 | 3 | 4 | 5 | 6 |
Price($) | 12 | 14 | 10 | 18 | 20 | 25 |
table 26
Grade | 1 | 2 | 3 | 4 | 5 | 6 |
Amount produced | 2 | 3 | 1 | 1.5 | 2 | 3 |
table 27
Grade | 1 | 2 | 3 | 4 | 5 | 6 |
Maximum demand | 20 | 30 | 40 | 35 | 25 | 50 |
table 28
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 |
table 29
Grade | 1 | 2 | 3 | 4 | 5 | 6 |
Cost of Disposition ($) | 3 | 2 | 3 | 2 | 4 | 2 |
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.