Example: Blending Problem


    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.
  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: