Raptor Fuels produces three grades of gasoline - Regular, Premium and Super. ALl

Question

Raptor Fuels produces three grades of gasoline - Regular, Premium and Super. ALl of these are produced by blending 2 types of crude oil - Crude A and Crude B. The two types of crude oil contain specific ingredients which help in determining the octane rating of gasoline. THe important ingredients and the costs are contained in the following tabble.

In order to achieve the desired octane ratings, at least 42% of the Regular gasoline should be Ingredient 1; at least 44% of Premium gasoline must be Ingredient 1 and at least 48% of Super gasoline must be Ingredient 1. Due to current contract committments, Raptor Fuels must produce at least 25,000 gallons of Regular, at least 18,000 gallons of Premium and at least 15,000 gallons of Super.

FOrmulate a linear program that could be used to determine how much of Crude A and Crude B should be used in each of the gasolines to meet the demands at minimum cost. What is the minimum cost? How much of Crude A and Crude B are used in each gallon of the different types of gasoline? Formulate this problem as a Linear Program and use Solver to find the answers.

PLEASE SHOW ALL WORK AND SCREENSHOTS OF EXEL. I KNOW to USE SOLVER BUT I WANT TO SEE WHAT THE FORMULAS LOOK LIKE.

Explanation / Answer

Solution:

This is a resource allocation problem in which optimal ingredient mix needs to be determined in order to minimize costs and meet regulations Variables: Crude A Crude B Regular x1 x2 Premium y1 y2 Super z1 z2 X1 represents that regular has been produced using x1 gallons of Crude A and similarly y2 represents that premium has been prepared by using y2 gallons of Crude B and so on... Objective Function: Minimize Total Cost 0.42*(x1+y1+z1) + 0.47*(x2+y2+z2) => Total cost needs to be minimized Production COnstraints: x1 + x2 >= 20,000 =>Raptor Fuels must produce as least 20,000 gallons of Regular y1 + y2 >= 15,000 =>Raptor Fuels must produce as least 15,000 gallons of Premium z1 + z2 >= 10,000 =>Raptor Fuels must produce as least 10,000 gallons of Super Ratings Constraint: 0.4x1 + .52x2 >= 0.41(x1+x2) => 0.11x2 - 0.01x1 >= 0 =>At least 41% of Regular gasoline should be Ingredient.

Let the amount of Crude A be A and the amount of Crude B be B,Ingredient 1 be I,Other Ingredient be O,
A 0 B 376.9230769
Constraints 19600   A*0.4+B*0.52>=20000*0.41+15000*0.44+10000*0.48=19600 180.9230769   .6A+.48B<=20000*.59+15000*.56+10000*.52      

Minimize 177.1538462   A*0.42+B*0.47  

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