Example:
Blending Problem
1.Text:
Various grades of gasoline are obtained by blending
together certain blending gasolines that are the direct output of the refinery
operations. In an actual refining operation, there are many blending gasolines,
many final-product gasolines (e.g., various grades of aviation and motor
gasoline), and many characteristics for example, octane rating, vapour
pressure, sulphur content, and gum content. In this simplified example,
we assume that a refinery has available only two types of blending gasoline,
whose characteristics are in Table 1. These blending gasolines may be mixed
to produce two final products, aviation gasoline and motor gasoline. The
required characteristics of these final products are in Table 2. The firm
wishes to maximise revenue from the sale of final product gasoline.
2.Tables:
| |
Octane |
Vapour |
Maximum available
(barrels) |
| BG1 |
104 |
5 |
30 000 |
| BG2 |
94 |
9 |
70 000 |
Table 1: Characteristic of
blending gasolines
| |
Octane |
Vapour |
Maximum sails
(barrels) |
Cost ($ per
barrel) |
| Aviation gasoline |
102 |
6 |
20 000 |
48,50 |
| Motor gasoline |
96 |
8 |
Any amount |
37,20 |
Table 2: Characteristic of final
product gasolines
Note: When gasolines are mixed together, the
resulting mixture has an octane and a vapour pressure in proportion to
the volume of each gasoline mixed. For example, if 1,000 barrels of blending
gasoline BG1 were mixed with 1,000 barrels of blending gasoline BG2, the
resultant gasoline would have an octane rating of 99:
