6 Two competing firms must simultaneously determine how much of a product to produce. The total profit earned by the two firms is always $1,000. If firm 1’s production level is low and firm 2’s is also low, then firm 1 earns a profit of $500; if firm 1’s level is low and 2’s is high, then firm 1’s profit is

$400. If firm 1’s production level is high and so is firm 2’s, then firm 1’s profit is $600; but if firm 1’s level is high while firm 2’s level is low, then firm 1’s profit is only $300. Find the value and optimal strategies for this constant-sum game.