Problem $4(20\%).$ This problem is based on problem $7\mathrm{.}3-4$ of chapter $7$ of the

Introduction to Operations Research, Hillier and Lieberman $11$ ed textbook. Refer to

problem $7\mathrm{.}3-4$ in the textbook and use SAS to solve the problem. Attach all the SAS

outputs below. Do not attach the full SAS$-$screen.

$1\mathrm{.}1$ Write out the mathematical model

$1\mathrm{.}2$ Use SAS to solve the problem and write out the objective value and the optimal solution.

Attach the SAS outputs below.

$1\mathrm{.}3$ Do sensitivity analysis and identify the allowable range for each cj coefficient. Explain

the allowable range for each cj coefficient. Attach the SAS outputs below.

$1\mathrm{.}4$ Increase both cj coefficients, solve the problem again, and make sure that the optimal

solution does not change. Explain the method you used to solve the problem, so the

optimal solution is the same as that in section $4\mathrm{.}2.$ Write out the objective value and the

optimal solution.Use SAS to solve the parametric programming problem below. Attach all the SAS

outputs below. Do not attach the full SAS$-$screen.

Maximize $Z()=(10-)x_1+(12+)x_2+(7+2)x_3$

subject to

$x_1+2x_2+2x_{3}30$

$x_1+x_2+x_{3}20$

and

$x_{1}0,x_{2}0,x_{3}0.$

Solve the problem when $=0.$ Write out the objective value and the optimal

solution. Attach the SAS outputs below.

Solve the problem when theta $=5.$ Write out the objective value and the optimal

solution. Attach the SAS output below.

Solve the problem when theta $=5\mathrm{.}1.$ Write out the objective value and the optimal

solution. Attach the SAS output below.

Solve the dual problem when theta $=0.$ Write out the mathematical model,

objective value and the optimal solution. Attach the SAS output below.

Solve the dual problem when theta $=5.$ Write out the objective value and the

optimal solution. Attach the SAS output below.