The choices are of the form $(x; y)$ where $x$ represents the amount of time you have left to live, say anywhere from $0$ to $50$ years, and $y$ represents the amount of time you have left to work, again anywhere from $0$ to $50$ years. Both $x$ and $y$ are continuous amounts of time, and certainly $x \geq y$. In general you prefer to live longer and work less, but you always prefer to live longer no matter how long you will work.
Is it possible to represent your preferences with a single (real-valued) number? That is to say, is there a utility function $u(x; y) : (x; y)\to R$?
Your preferences on different combinations of $x$ and $y$ are lexicographic, with the small twist that you prefer $y$ to be small instead of large.
If there existed a utility function $u$ for this preference, then any value $u(a,b)$ would have to be preceeded by an uncountable number of intervals $[u(x,y_1),u(x,y_2)]$. This is not possible, since you can pick a rational number from each interval, and there are only countably many rationals.