question)

My answer through lindo shows that the maximum profit is 71400, but i think the chegg textbook solution is indicating 31400 or something.

solution i thought, was

Max 3ra + 5rb + 0rc + 6rd + 9pa + 11pb + 6pc + 12pd + 1da +3db - 2dc + 4dd

st

ra + pa + da 3000 pa + pb + pc + pd > 3000 da + db + dc + dd > 3000 0.6ra - 0.4rb - 0.4rc - 0.4rd > 0 0.8rb - 0.2ra - 0.2rc - 0.2rd 0 0.6pc - 0.4pa - 0.4pb - 0.4pd > 0 0.5db - 0.5da - 0.5dc - 0.5dd 0

end

i dont know why.. please tell me where is wrong with my answer.

Type or paste question here

5. A refinery blends four petroleum components into three grades of gasoline - regular, premium, and low-lead. The maximum quantities available of each component and the cost per barrel are shown below: Component 2 3 4 Maximum Barrels Available/Day 5000 2400 4000 1500 Cost/Barrel (9) 9 7 12 6 To ensure that each gasoline grade retains certain essential characteristics, the refinery has put limits on the percentage of the components in each blend. The limits as well as the selling prices for the various grades are as follows: Grade Component Specifications Selling Price/Barrel (5) Regular Not less than 40% of 1 12 Not more than 20% of 2 Not more than 30% of 3 Premium Not less than 40% of 3 18 Low-Lead Not more than 50% of 2 10 Not less than 10% of 1 The refinery wants to produce at least 3000 barrels of each grade of gasoline. Management wishes to determine the optimal mix of the four components that will maximize profit. Formulate a linear programming model for this problem and solve using the computer. E UD 5)