
3.5: Review Problems


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).