Refinery Gasoline Blending

A petroleum refinery manufactures three types of gasoline(1) Super, (2) Premium and (3) Regular.

Eachtype of gasoline isproducedbyblending of gasoline produced from distillation ofthreetypesofcrudeoil(crude1,crude2andcrude3).

The salespriceperbarrelofgasolineandthepurchasepriceperbarrelof crudeoilaregivenbelow:

Gasoline Salepriceperbarrel

• Super$70
• Premium$60
• Regular $50

Crude oilPurchasePriceperbarrel

Crude1                   $45

Crude2                   $25

Crude3                   $20

• The company canpurchaseupto5000barrelsofeachtypeofcrudeoildaily.

The threetypesofgasolinedifferintheiroctaneratingandsulfur content.

• The gasoline from crudeoilblended toform Super gasoline musthaveanaverageoctaneNoof atleast90andcontainatmost1%
• Thegasoline from crude oilblendedtoformPremium gasoline musthaveanaverageoctaneNoofatleast89andcontain atmost2%sulfur.
• The gasolinefrom crude oil blendedtoformRegular gasolinemusthaveanoctaneNoofatleast87 andcontainatmost1%sulfur.
• The octaneNo andthesulfur contentof gasolineobtained fromthreetypesofcrude oil aregivenbelow:

Crude oilOctane NO.Sulfur content

Crude 1               92                     0.5 %

Crude 2               86                     2.0 %

Crude 3               90                     3.0 %

• Itcosts$4totransformonebarrelof oilintoonebarrelofgasolineusing distillation,
• The companycan produceupto14,000barrelsofgasolinedaily.
• The company’scustomersrequirethefollowingamountsofeachgasoline:
• Super :3000bbl/d
• Premium :2000 bbl/d
• Regular :1000bbl/d.

Thecompanyconsidersitanobligationtomeet thesedemands.

 

Required:

 

1. Formulatethe linear programing problem thatwillmaximize
2. Solve the problem to determine the barrelsused from each crude to make each gasoline type per day and the daily profit.
3. Show using graph the effect of the following on the daily profits.
4. The selling price of the 3 types of gasoline
5. The purchasing price of the 3 types of crude oil.
6. The maximum allowable sulfur content of Regular gasoline.
7. The minimum required ON of Regular gasoline.