Problem $5.(2\mathrm{.}15$ in text book$)$

Consider the following linear program:

minz$(x_1,x_2)=2x_1+x_2$

$3x_1+x_{2}1$

$x_1+4x_{2}2$

$-x_1+x_{2}1$

subject to

Plot the feasible region, the contours of the objective function, the direction perpendicular to

curves of binding constraints, and the gradient of the objective function at the minimum point.