2 A total of 90,000 customers frequent the Ruby and the Swamp supermarkets. To induce customers to enter, each store gives away a free item. Each week, the giveaway item is announced in the Monday newspaper. Of course, neither store knows which item the other store will choose to give away this week. Ruby’s is considering giving away a carton of soda or a half gallon of milk. Swamp’s is considering giving away a pound of butter or a half gallon of orange juice. For each possible choice of items, the number of customers who will stop at Ruby’s during the current week is shown in Table 50. Each store wants to maximize its expected number of customers during the current week. Use game theory to determine an optimal strategy for each store and the value of the game. Interpret the value of the game.

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TABLE 50 Swamp Chooses Ruby Chooses Butter Orange Juice Soda 40,000 50,000 Milk 60,000 30,000