Problem $1$

Consider the following linear programming problem.

Minimize $Z=5x_1+6x_2+3x_3,$

subject to:

$5x_1+5x_2+3x_{3}50$

$x_1+x_2-x_{3}20$

$7x_1+6x_2-9x_{3}30$

$5x_1+5x_2+5x_{3}35$

$2x_1+4x_2-15x_{3}10$

$12x_1+10x_{2}90$

$x_2-10x_{3}20$

$x_1,x_2,x_{3}0$

a$)$ In an Excel workbook, solve the problem by using the Solver. Genefate the Solver sensitivity and ans

b$)$ In this Word document, write the mathematical formulation of the dual problem. Generate a sensiti of the dual problem.

c$)$ Solve the dual problem in anather sheet of the same Excel file.

d$)$ In this Word document, describe whether the solution of the dual problem offers computational ad explain why. Submit the Excel workbook as a separate attachment.