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# 3.5: Review Problems

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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).