Consider the game having the following payoff table:

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

$($a$)$ Use the approach described in Sec. $15\mathrm{.}5$ to formulate the problem of finding optimal mixed strategies according to the mini$-$ max criterion as a linear programming problem. $($b$)$ Use the simplex method to find these optimal mixed strategies. $(25$pt$)$