For the following three problems, provide your written solutions within this template Do not create a new file.

Show all steps used in arriving at the final arswers, Incomplete solutions will receive partial crodit.

Provide formulas using Equation Editor and diagrams using Drawing Tool.

Use the Solver to obtain computer solutions in an Exod workbook.

Submit the Word and Excel workbook$($s$)$ separately as attachments.

Problem $1$

Consider the following linear programmirg problem.

Minimize $x-5x_1+6x_2+3x_3$

Subject $to$:

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

$x_1+x_2-x_{1}20$

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

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

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

$12x_1+10x_{2}90$

$x_2-10x_{1}20$

$x_1,x_7,x_{1}0$

a$)$ In an Excol workbook, solve the problem by using the Solver. Generate the Solver semutivity and answer reports.

b$)$ In this Word document, write the mathematical formulation of the dual problem Generate a sensitivity report of the dual problem:

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

d$)$ In this Word decument, describe whether the solution of the dual problum offers cemputational advantage and explain why, Submit the Exrel workbook as a separate attachment.