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).

Contributor

• David Cherney, Tom Denton, and Andrew Waldron (UC Davis)