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Mathematics LibreTexts

3.5: Review Problems

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  • Page ID
    1842

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    1.    Maximize \(f(x,y)=2x+3y\) subject to the constraints
    $$
    x\geq0\, ,\quad y\geq0\, ,\quad x+2y\leq2\, ,\quad 2x+y\leq2\, ,
    $$
    by 

    a)    sketching the region in the \(xy\)-plane defined by the constraints and then checking the values of \(f\) at its corners; and,

    b)    the simplex algorithm (\(\textit{Hint:}\) introduce slack variables).

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