Hypothetical reasoning is an important framework for knowledgebased systems because it is theoretically founded and it is useful for many practical problems. Since its inference time grows exponentially with respect to problem size, its efficiency becomes the most crucial problem when applying it to practical problems. Some approximate solution methods have been proposed for computing cost-based hypothetical reasoning problems efficiently; however, for humans their mechanisms are complex to understand. In this paper, we present an understandable efficient method called SL (slide-down and lift-up) method which uses a linear programming technique, namely simplex method, for determining an initial search point and a non-linear programming technique for efficiently finding a near-optimal 0-1 solution. To escape from trapping into local optima, we have developed a new local handler which systematically fixes a variable to a locally consistent value when a locally optimal point is detected. This SL method can find a near-optimal solution for cost-based hypothetical reasoning in polynomial time with respect to problem size. Since the behavior of the SL method is illustrated visually, the simple inference mechanism of the method can be easily understood.