Humans are prone to invent games to pass the time. Bored warehouse workers such as the one

depicted in Sokoban have taken to using the package scales as a way to pass the hours in

between the loading and unloading of shipments. The game involves two players each trying

to get the best possible score by taking turns placing packages of unknown weight on the scales.

The packages available to player $1$ weight $2,5,$ and $11$ kilograms and those for player $2$ are $3,$

$7,$ and $17$ kilograms $($although they do not know it$).$ Each player gets a chance to place one

package on the scale and the final score is assigned based on the total weight. Player $1$ is trying

to get the highest possible score while player $2$ is trying to get the lowest score. $\begin{array}{cc}\text{F}\text{i}\text{n}\text{a}\text{l}\text{W}\text{e}\text{i}\text{g}\text{h}\text{t}& \text{S}\text{c}\text{o}\text{r}\text{e}\\ 5kg& 5\\ 9kg& 7\\ 19kg& 2\\ 8kg& 15\\ 12kg& 12\\ 22kg& 14\\ 14kg& 10\\ 18kg& 11\\ 28kg& 9\end{array}$ a$)$ Provide a high$-$level formal definition of the game suitable for use by an

adversarial search agent.

b$)$ Complete the following minimax tree which captures the optimal play for the

game. Indicate how the minimax approach could be improved.