Blending problem
A heating-oil distributor blends two grades of heating oil (regular and non toxic) from three products (called distillates 1, 2, and 3) produced in the crude-oil refining process. The distillates are purchased from a local refinery. The heating oils are simply blends of the three distillates, but must conform to certain specifications particularly with regard to their sulfur content and vapor pressure. The data concerning the heating oils are shown in Table 1 and the data for the distillates is shown in Table 2. We assume that a blend of distillates has specifications (sulfur content, vapor pressure) equal to the weighted average of the components. This assumption is not in general true, for example, with octane rating.
maximum minimum maximum maximum
sulfur vapor distillate 3 selling monthly
content pressure content price sales
Regular 14 grams 6 units 80 % $12.00 10,000 barrels
Non toxic 8 grams 12 units 30 % 16.00 4,000 barrels
Table 1. Heating-Oil Data
sulfur vapor selling available
content pressure price monthly
Distillate 1 6 grams 16 units $10.00 3,000 barrels
Distillate 2 10 grams 8 units 14.00 2,000 barrels
Distillate 3 18 grams 4 units 6.00 10,000 barrels
Table 2. Distillate Data
Formulate LP model to find out how many barrels of each type of heating oil to produce to maximize profit while satisfying all the requirements.