Problem $2.(50$ points$)$ Formulate the dual of the linear programming formulation for the Fibre Optic Cabling Problem. Use general algebraic notation and the format studied in ISE $2404$ to present your dual model. Using AMPL and Gurobi, solve this dual linear program and report the optimal solution value and the optimal solution.

Problem $3.(50$ points$)$ Perform a thorough sensitivity analysis of your $($primal$)$ linear programming formulation by modifying cost coefficients, constraint matrix, and$/$or RHS of the constraints. $[$This problem requires creativity in modifying the data parameters such that this analysis provide the management some insight about its operations. Please present your results and observation, using charts and graphs with complete description, in the report assuming that your team is a consultant firm seeking consultancy contract from this cable company.$]$