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Linear Programming

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OKay My question is:
Two factories manufacture 3 different grades per paper. the company that owns the factories has contracts to supply at least 16 tons of low grade, 5 tons of medium grade, and at least 20 tons of high grade paper. It cost $1000 per day to operate the first factory and 2000 per day to operate the second. Factory 1 produces 8 tons of low grade, 1 ton of medium grade, and 2 tons of high grade paper in day's operation. Factory 2 produces 2 tons of low grade, 1 ton of medium grade and 7 tons of high grade per day. how many days should each factory be in operation in order to fill the most economically?

Also i have to assign variables to x and y and state a goal plus represent the goal with an equation
then i have to write inequalities that represent the restrictions of this problem in a chart. Then i have to grade the system of inequalities, shade the solution region, and use corner points to analyze data and find the solution. Finally I write my solution in a complete sentence.
Help?

  • Linear Programming - ,

    So the instructions seem to be clear. Do you have a problem, or where is the problem if there is any?

  • Linear Programming - ,

    It's just I'm stuck at picking out what i need and such.. Not very good with word problems..

  • Linear Programming - ,

    You can take the question and split it up into constraints and costs.

    Requirements:
    "supply at least 16 tons of low grade, 5 tons of medium grade, and at least 20 tons of high grade paper."
    So minimum quantities = (16,5,20)
    Supplied by Factory 1, F1 = (8,1,2)/$1000
    Supplied by F2 = (2,1,7)/$2000

    So the constraints are:
    8F1+2F2 ≥ 16
    F1+F2 ≥ 5
    2F1+7F2 ≥ 20
    F1 ≥ 0
    F2 ≥ 0

    Cost=1000F1+2000F2

    Your graph will have F1 in the x-axis, F2 in the y-axis. Plot the constraint equations, and shade the solution (feasible) region. Find the optimal solution.

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