Use the solution report provided for the linear program below to answer the following questions:

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

value of the objective function?

b$)$ What will be the new maximum value of the objective function if the right$-$hand side of the $2^{nd}$

constraint is decreased by $2?$ Can you answer this question if it is increased by $6?$ Explain your

answers.

c$)$ Use the $100\%$ rule to check if the optimal solution will change if the right$-$hand side of the $2^{nd}$

constraint is increased by $2$ and the right$-$hand side of the $3^{rd}$ is decreased by $1.$

max$2x_1-2x_2+3x_3$

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

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

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

$x_1,x_2,x_{3}0$

Objective Cell $($Max$)$

Variable Cells

Constraints