Question: A professional gambler plays a game that requires dividing up his bet into four choices. The game has three possible outcomes. The table below provides the net payoff for every $1 he bets (a positive payoff is a gain for him; a negative payoff is a loss for him).

The gambler has a total of $1,000 to bet. The exact outcome of the game is not known a priori. The probabilities of the outcomes are not available. Because of the uncertainty, the gambler’s strategy is to maximize the minimum return produced by the three outcomes.

a. Formulate algebraically the problem as a linear program, by defining the decision variables, the objective function and the constraints.

b. He wants to bet the entire $1,000 only once. Using Solver, find the amount of bet that he has to allocate for each choice. Will he win or lose?