ExerciseSet1.pdf - Linear Programming 2013-2014 Exercise...

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Linear Programming 2013-2014 Exercise Set 1 Modeling linear programming problems Exercise 1 Production of fuel oil from distillates A distributor of oil sells two types of fuel oil (normal and unleaded) blended from three components (distillate 1, 2 and 3). These distillates are distilled from crude oil and are purchased from a refinery. The two fuel oils are simple blends from the three distillates, but certain properties are required with respect to sulfur degree and gas pressure. The requirements are given in the table below: maximum sulfur degree minimum gas pressure (grams/barrel) Normal 14 6 Unleaded 8 12 Furthermore, it is required that the normal (resp. unleaded) fuel oil should consist of at most 80% (resp. 30%) of distillate 3. The distributor has the following sales data corresponding to the two types of fuel oil: selling price maximum sales (euro/barrel) (barrels/month) Normal 12 10,000 Unleaded 16 4,000 Finally, the data about sulfur degree and gas pressure together with purchasing cost and availability are shown in the table below. We assume that the desired properties (sulfur degree, gas pressure) of each type of fuel oil equals the weighted average of the properties of the components. sulfur degree gas pressure purchasing cost maximum availability (gram/barrel) (euro/barrel) (barrels/month) Distillate 1 6 16 10 3,000 Distillate 2 10 8 14 2,000 Distillate 3 18 4 6 10,000 1
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