A small software production company wants to maximize the benefit of the time and money spent by its staff in working on development projects. It produces software that is roughly classified as one of three types, increasing in value and also difficulty from one type to the next. Type 1 projects are half as valuable as type 2 projects, which are in turn half as valuable as type 3 projects. Each type 1 project requires two programmers, and 40 hours of planning and documentation over the span of a month; each type 2 project requires five programmers and 60 hours of time, and each type 3 project requires eight programmers and 90 hours of time. How should the company allocate its resources for a month's work if it has 30 programmers and 300 hours of time? Can non-integer solutions make sense in this problem; and if so, how?