The Massoil Refinery processes two different kinds of crude oil, Venezuelan and Saudi to produce two...

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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 and the type of crude oil that is being processed. 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 .45 units of Light product, .52 units of Heavy product and .03 units of waste. Light product fraction. Heavy product fraction Unusable product fraction SHORT PROCESS Venezuelan Saudi .45 .52 .03 .60 .36 .04 REGULAR PROCESS Venezuelan Saudi .68 .32 .00 .49 .50 .01 Saudi crude costs $22 per unit while Venezuelan crude costs $21 per unit. The short process costs $2.10 per unit processed while the regular process costs $2.50 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? In this problem, there are four primary decision variables representing the amounts of each type of crude oil processed in each mode (4 combinations) but many more dependent variables can be used that make the formulation elegant, easy to understand and verify, and to provide useful output information such as crudes to buy, amounts to process in each mode, and final product amounts produced. For a hint to start the formulation of this problem, see to the hint document where I provide insight into it and work through part of the formulation process. 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 and the type of crude oil that is being processed. 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 .45 units of Light product, .52 units of Heavy product and .03 units of waste. Light product fraction. Heavy product fraction Unusable product fraction SHORT PROCESS Venezuelan Saudi .45 .52 .03 .60 .36 .04 REGULAR PROCESS Venezuelan Saudi .68 .32 .00 .49 .50 .01 Saudi crude costs $22 per unit while Venezuelan crude costs $21 per unit. The short process costs $2.10 per unit processed while the regular process costs $2.50 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? In this problem, there are four primary decision variables representing the amounts of each type of crude oil processed in each mode (4 combinations) but many more dependent variables can be used that make the formulation elegant, easy to understand and verify, and to provide useful output information such as crudes to buy, amounts to process in each mode, and final product amounts produced. For a hint to start the formulation of this problem, see to the hint document where I provide insight into it and work through part of the formulation process.