Professor Proof is trying to arrange for the implementation in a computer program of his latest operations research algorithm. He 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 0.3 as productive, and undergraduates, 0.2. Proof has only 164 hours of his own time to devote to the effort, and he knows from experience that undergraduate programmmers require more supervision than graduates, and graduates more than professionals. In particular, he estimates that he will have to invest 0.2 hour of his own time per hour of undergraduate programming, 0.1 hour of his time per hour of graduate programming, and 0.05 hour of his time per hour of professional programming. (An optimization output appears in Table 6.8.)

(a) Briefly explain how this problem can be modeled by the LP min 4x1 + 10x2 + 25x3 s.t. 0.2x1 + 0.3x2 + x3 Ú 1000 0.2x1 + 0.1x2 + 0.05x3 … 164 x2 … 500 x1, x2, x3 Ú 0

(b) through

(d) as in Exercise 6-1.