Chemical Processing $-$ Input$/$Output Processing $-$ Blending

The Massoil 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 the 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 $\mathrm{.}45$ units of Light product, $\mathrm{.}52$

units of Heavy product and $\mathrm{.}03$ units of waste.

Saudi crude costs $$22$ per unit while Venezuelan crude costs $$21$ per unit. The

short process costs $$2\mathrm{.}10$ per unit processed while the regular process costs $$2\mathrm{.}50$ per

unit. During any week, Massoil can process at most $10,000$ units of crude at the regular

mode and $13,000$ units of crude at the short mode.

The respective market values of light and heavy products are $$29$ and $$27$ per

unit, while the unusable product is disposed of at the cost of $$1$ per unit. Formulate a LP

problem that optimally determines the amounts of crudes to buy and the processes to run.

What are the optimal purchasing and operating decisions?