A petroleum refinery manufactures three types of gasoline(1) Super, (2) Premium and (3) Regular.
Each type of gasoline is produced by blending of gasoline produced from distillation ofthreetypesofcrudeoil(crude1,crude2andcrude3).
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Write My Essay For MeThe 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:
- Formulatethe linear programing problem thatwillmaximize
- Solve the problem to determine the barrelsused from each crude to make each gasoline type per day and the daily profit.
- Show using graph the effect of the following on the daily profits.
- The selling price of the 3 types of gasoline
- The purchasing price of the 3 types of crude oil.
- The maximum allowable sulfur content of Regular gasoline.
- The minimum required ON of Regular gasoline.
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