The Analytic Hierarchy Process (AHP) provides a way to rank the alternatives of a problem by deriving priorities. A question that occurs in practice is: what is the best combination of alternatives that has the largest sum of priorities and satisfies given constraints? This leads one to consider the interface between the AHP and the combinatorial approach inherent in Linear Programming (LP). The priorities of the alternatives often serve as coefficients of the objective function of an LP problem. The constraints are determined from existing measurements, such as the range for the number of employees needed and the salaries required for various jobs. Another way to use the AHP might be to determine the coefficients of the constraints. This paper addresses the first half of the problem. Through various examples, we show how to apply the absolute measurement mode of the AHP together with LP to optimize human resource allocation problems. For example, one can determine which positions to fill, or which mix of candidates to hire. We also give an example of how to allocate resources to maximize the returns to a corporation of its training programs. Finally, we show that the combined AHP and LP model is capable of solving hiring problems involving synergy, such as when two persons with different complementary skills work as a team.