max$2x_1-2x_2+3x_3$

$s.t.$: $-x_1+x_2+x_{3}4$

$2x_1-x_2+x_{3}2$

$x_1+x_2+3x_{3}12$

$x_1,x_2,x_{3}0$

Constraints

Use the solution report to answer the following questions:

a$)$ What are the values of the decision variables at the optimal solution?

b$)$ Is the solution unique? Explain your answer.

c$)$ What is the optimal solution of the dual problem?

d$)$ Suppose that the coefficient of variable $x_1$ in the objective function in increased by $0\mathrm{.}5$ and the

coefficient of $x_2$ is increased by $1.$ Apply the $100\%$ rule to examine if these two simultaneous

changes will affect the optimal solution.