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Math Help - Constraint Equation

  1. #1
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    Constraint Equation

    John can make a profit of $7 per chair and $12 per desk. He has at most 48 hrs working time available. It takes 3 hrs to make a chair and 2 hrs to make a desk. Write the objective function and constraints necessary to determine how many chairs and desks he should make to maximize profit.

    Help please!!!

    X=Chairs
    Y=desks

    I cant figure out the constraints other than:

    3x+2y<48
    7x+12y>0
    x>0
    y>0
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  2. #2
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    Lexington, MA (USA)
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    Hello, JennM!

    You need a small adjustment . . .


    John can make a profit of $7 per chair and $12 per desk.
    He has at most 48 hrs working time available.
    It takes 3 hrs to make a chair and 2 hrs to make a desk.
    Write the objective function and constraints necessary to determine
    how many chairs and desks he should make to maximize profit.

    x = chairs . y = desks

    I cant figure out the constraints other than:

    3x+2y\:<\:48
    7x+12y\:>\:0 . . . . no
    x\:>\:0,\;y\:>\:0

    Objective function: . P \:=\:7x+12y . (profit)


    Constraints: . \begin{Bmatrix}3x + 2y \:\leq \:48 \\<br />
x \:\geq \:0 \\ y \:\geq \:0 \end{Bmatrix}


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  3. #3
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    I was trying to get the Greater n less than or equal to signs... Couldnt find them. So basically I had the answer but was confused thanks for the help
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