Important: For questions involving the simplex algorithm clearly write the following at each

simplex iteration:

a$.$ The simplex tableau

b$.$ The current basic feasible solution along with the sets of basic and nonbasic variables

c$.$ The results of the ratio test

d$.$ The entering variable, and the leaving variable

Question $1(5$pts$)$: Consider the following LP:

max,$z=2x_1+3x_2+2x_3+2x_4$

$s.t.2x_1+x_{2}2$

$x_3+x_{4}7$

$x_1,x_2,x_3,x_{4}0$

a$.$ Solve the LP using the simplex method.

b$.$ Are there multiple optimal solutions? If so$,$ generate a second optimal solution. If not, explain

why.