Consider a two$-$person game problem with the following payoff matrix:

Player B

Player

A

B$1$ B$2$ B$3$

A$1121$

A$2122$

A$3343$

$($i$)$ What is the objective of player A$?$ Write down the concerned linear

programming problem for player A$.$

$($ii$)$ What is the objective of player B$?$ Write down the concerned linear

programming problem for player B$.$

$($iii$)$ Applying the linear programming$-$based Simplex method, determine the game

value as well as the optimal strategies for both players.