Consider the two$-$person, zero$-$sum game having the following payoff table.

$\backslash$table$[[$Strategy$,$Player $2],[1,2,3],[$Player $1,1,1,3,1],[2,3,-2,-1],[3,1,4,0]]$

a$)$ Determine the optimal strategy and payoff for each player by successively eliminating dominated strategies. Show your reasoning and the order in which you eliminated strategies.

b$)$ Set up a LP model to find the optimal strategy for Player $1.$ Then, solve the LP problem by LINGO. Include the LINGO output screen in your answer.