Suppose a family has saved enough for a 10 day vacation (the only one they will be able to take for 10 years) and has a utility function U = V^1/2 (where V is the number of healthy vacation days they experience). Suppose they are not a particularly healthy family and the probability that someone will have a vacation ruining illness (V = 0) is 20%.

1. What is the greatest (integer) number of vacation days the family would be willing to give up in order to guarantee a healthy vacation?