Use the solution report provided for the linear program in the next page to answer the questions

below:

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

b$)$ Given the solution shown in the reports, what are the slacks of the constraints?

c$)$ Calculate the optimal objective function value if the right$-$hand side of the $1^{st}$ constraint is in$-$

creased from $5$ to $5\mathrm{.}1.$ Also, calculate the optimal objective function value if the right$-$hand side

of the $2^{nd}$ constraint is increased from $4\mathrm{.}7$ to $4\mathrm{.}8.$

d$)$ Use the $100\%$ rule to check if the optimal solution will change if the objective function is changed

to $-x_1+2x_2+3x_3.$