Quantitative Analysis for Management

Raptor Fuels arrive ats three grades of gas pedal Regular, Premium, and top-notch. all told of these ar produced by blending both types of jolting oil Crude A and Crude B. The two types of crude curb specific ingredients which help in determine the octane rating of petrol. The important ingredients and the costs are contained in the following table pic .. In order to achieve the desired octane ratings, at least(prenominal) 41% of Regular petrol 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 trustworthy contract commitments, Raptor Fuels must produce as least 20,000 gallons of Regular, at least 15,000 gallons of Premium, and at least 10,000 gallons of Super. Formulate a linear program that could be utilize to determine how much(prenominal) of Crude A and Crude B should be utilize in all(prenominal) of the gasolines to meet the demands at the minimum cost. What is the minimum c ost? How much of Crude A and Crude B are use in each gallon of the different types of gasoline? consequence Let A1 = gallons of crude A utilize in Regular A2 = gallons of crude A apply in Premium A3 = gallons of crude A used in Super B1 = gallons of crude B used in Regular B2 = gallons of crude B used in Premium B3 = gallons of crude B used in Super play down cost = 0. 42A1 + 0. 42A2 + 0. 42A3 + 0. 47B1 + 0. 47B2 + 0. 47B3 Subject to 0. 40A1 + 0. 52B1 ( 0. 41(A1 + B1) 0. 40A2 + 0. 52B2 ( 0. 44(A2 + B2) 0. 40A3 + 0. 52B3 ( 0. 8(A3 + B3) A1 + B1 ( 20,000 A2 + B2 ( 15,000 A3 + B3 ( 10,000 A1, A2, A3, B1, B2, B3 ( 0 The resultant role is A1 = 18,333. 33 gallons of crude A used in Regular A2 = 10,000 gallons of crude A used in Premium A3 = 3,333. 33 gallons of crude A used in Super B1 = 1. 666. 67 gallons of crude B used in Regular, B2 = 5,000 gallons of crude B used in Premium B3 = 6,666. 67 gallons of crude B used in Super total cost = $19,566. 67.