The Sebastopol Refinery processes two different kinds of crude oil, Venezuelan and Saudi, to
produce two general classes of products, Light and Heavy. Either crude oil can be processed by
either of two modes of processing, Short or Regular. The processing cost and amounts of Heavy
and Light produced depend upon the mode of processing used and the type of crude oil used.
Costs vary, both across crude oils and across processing modes. The relevant characteristics are
summarized in the table below. For example, the short process converts each unit of Venezuelan
crude to 0.45 units of Light product, 0.52 units of Heavy product, and 0.03 units of waste.
Short Process Regular Process
Venezuela Saud Venezuela Saud
Light prod 0.45 0.60 0.49 0.68
Heavy prod 0.52 0.36 0.50 0.32
Unused prod 0.03 0.04 0.01 0.00
Saudi crude costs $20 per unit, whereas Venezuelan crude is only $19 per unit. The short
process costs $2.50 per unit processed, while the regular process costs $2.10 per unit. Sebastopol
can process 10,000 units of crude per week at the regular rate. When the refinery is running the
Short process for the full week, it can process 13,000 units per week.
The refinery may run any combination of short and regular processes in a given week.
The respective market values of Light and Heavy products are $27 and $25 per unit.
Formulate the problem of deciding how much of which crudes to buy and which processes to run
as an LP. What are the optimal purchasing and operating decisions?