Suppose a family is considering going to a hockey game, but the roads are covered in ice. The tickets were a gift and the family gets a value of from attending the game together, but incurs a cost of for driving on the hazardous roads. The family's utility function is given by . The family determines that the cost of driving on the icy roads is 1 unit ( ). What is the minimum value they must obtain from the attending the game in order for them to decide to go (what must be the value of )? (Hint: if they do not go to the game, they receive 0 and pay no costs).
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