Use the simplex method to find positive values of $x_1$

and $x_2$ that minimize

$f=10x_1+x_2$

subject to

$4x_1+x_{2}32$

$2x_1+x_{2}12$

$2x_1-x_{2}4$

$-2x_1+x_{2}8$

Sketch the points obtained by the simplex method

on a graph, indicating how the points progress

through Phases $1$ and $2$ to the solution.