Dr$.$ Stevens is trying to arrange for the implementation in a computer program of her latest operations research algorithm. She can contract with any mix of three sources for help: unlimited hours from undergraduates at $$4$ per hour, up to $500$ hours of graduate students at $$10$ per hour, or unlimited hours of professional programmers at $$25$ per hour. The full project would take a professional at least $1000$ hours, but grad students are only $30\%$ as productive, and undergraduates are only $20\%$ as productive.

Stevens has only $164$ hours of her own time to devote to the effort, and she knows from experience that undergraduate programmers require more supervision than graduates, and graduates more than professionals. In particular, she estimates that she will have to invest $0\mathrm{.}2$ hour of her own time per hour of undergraduate programming, $0\mathrm{.}1$ hour of her time per hour of graduate programming, and $0\mathrm{.}05$ hour of her time per hour of professional programming.