Xavier and Ying are partners in a course project. Xavier is the project leader and thus is the first to decide how many hours, hX, to put into the project. After observing the amount of time that Xavier contributes, Ying decides how many hours, hY, to contribute. Xavier's utility function is UX = 18(hX+hY)0.5 - hX, and Ying's utility function is UY = 18(hX+hY)0.5 - hY. Ying threatens not to work on the project. For Ying's threat to be credible, what is the smallest number of hours that Xavier must contribute to the project? How much time does Xavier contribute? Does Ying work on the project?