Question $4$

Consider the following problem.

minz$=-4x_1-6x_2+15,$

$2x_1+x_2,10$

$s.t.x_1,1$

$x_1,x_2,0$

a$.(5$ points$)$ Calculate the number of possible corner points.

b$.(25$ points$)$ Draw a graphical representation of the problem in terms of the original variables $x_1$ and $x_2,$ show the feasible region, highlight corner points, and indicate the path traversed by the simplex algorithm.