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Math Help - Solving Linear Problems with Excel

  1. #1
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    Solving Linear Problems with Excel

    I am working on this Problem below and I am having trouble coming up with one of the constraints.

    1) At a certain refinery, the refining process requires the production of at least two gallons of gasoline for each gallon of fuel oil. To meet the anticipated demands of winter, at least three million gallons of fuel oil a day will need to be produced. The demand for gasoline, on the other hand, is not more than 6.4 million gallons a day.

    If gasoline is selling for $1.90 per gallon and fuel oil sells for $1.50/gal, how much of each should be produced in order to maximize revenue?

    a) Formulate the linear programming model for the problem.
    b) Use the Graphical method to find the optimal solution. Show all steps.
    c) Use Excel Solver or LINDO to find the optimal solution. Copy and paste your entire solution from Excel or LINDO.


    This is what I have formulated so far:

    Max = 1.90x + 1.50y

    x<= 6400000
    y>= 3000000
    x,y>=0

    and I cant figure out how to formulate "the production of at least two gallons of gasoline for each gallon of fuel oil."

    Any help? and am I doing this correctly?
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  2. #2
    MHF Contributor

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    Re: Solving Linear Problems with Excel

    Quote Originally Posted by Cu09 View Post
    I am working on this Problem below and I am having trouble coming up with one of the constraints.

    1) At a certain refinery, the refining process requires the production of at least two gallons of gasoline for each gallon of fuel oil. To meet the anticipated demands of winter, at least three million gallons of fuel oil a day will need to be produced. The demand for gasoline, on the other hand, is not more than 6.4 million gallons a day.

    If gasoline is selling for $1.90 per gallon and fuel oil sells for $1.50/gal, how much of each should be produced in order to maximize revenue?

    a) Formulate the linear programming model for the problem.
    b) Use the Graphical method to find the optimal solution. Show all steps.
    c) Use Excel Solver or LINDO to find the optimal solution. Copy and paste your entire solution from Excel or LINDO.


    This is what I have formulated so far:

    Max = 1.90x + 1.50y
    This makes no sense at all until you have specified what "x" and "y" represent. I can tell, from the statement that "gasoline is selling for $1.90 per gallon and fuel oil sells for $1.50/gal", that you mean x to represent "amount of gasoline produced, in gallons" and y to represent "amount of fuel oil produced, in gallons" but you should say that before you write any equations. (Besides, it would shock your teacher!)

    x<= 6400000
    y>= 3000000
    x,y>=0

    and I cant figure out how to formulate "the production of at least two gallons of gasoline for each gallon of fuel oil."
    Exactly two gallons of gasoline for each gallon of fuel oil would be x= 2y so "at least" would be [latex]x\ge 2y[/latex].

    Any help? and am I doing this correctly?
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