Develop the Mathematical LP model for the following problem:

A gambler plays a game that requires dividing bet money among four choices. The game has three outcomes. The following table gives the corresponding gain or loss per dollar for the different options of the game.

The gambler has a total of $1500, which may be played only once. The exact outcome of the game is not known a priori. Because of this uncertainty, the gamblers strategy is to maximize the minimum return produced by the three outcomes. How should the gambler allocate the $1500 among the four choices? Solve the model using Solver or AMPL. (Hint: The gamblers net return may be positive, zero, or negative.)

\begin{tabular}{lrrrr} \hline & \multicolumn{4}{c}{ Return per dollar deposited in choice } \\ \cline { 2 - 5 } Outcome & 1 & 2 & 3 & 4 \\ \hline 1 & -3 & 4 & -7 & 15 \\ 2 & 5 & -3 & 9 & 4 \\ 3 & 3 & -9 & 10 & -8 \\ \hline \end{tabular}