Your question title mentions a "Normal Desktop Application", but your text talks about needing to apply knowledge of computational geometry and linear programming. Those are applications areas that have spawned huge, multi-decade research programs with massive societal consequences of any advance (recall, linear programming abstracts resource allocation). As a result, there are a lot of sophisticated approaches to solving problems in these areas that work very well.
A bad hire
- may not have even heard of these classes of problems,
- might not be familiar with the common solutions,
- probably wouldn't know about the better stuff that's out there (hint: most undergrads never hear about the fancy stuff, if they hear about the problems at all), and
- almost certainly would take ages to implement such things (considering that I've seen some of them give an entire graduate seminar in data structures fits, professor included).
In other words, think about whether you're really working on something pedestrian. If you are, great, hiring should be much easier. If you're not, hold out for someone who can do what you need.