The planning-from-observation paradigm is widely noticed as a novel robot-programming technique. It consists of two parts: (1) recognition of a human demonstration from observation as symbolic representation, i.e., a sequence of movement primitives and (2) execution of the same task. Symbolic representation enables a robot to achieve the same task even in a different environment. We already proposed a method to build a symbolic representation for an assembly task. However, for a robot to execute the task, it is necessary to adjust parameters of each movement primitive to generate appropriate trajectories of objects, especially a path which maintains one of any contact states. Many researchers have proposed methods to calculate such a path using a non-linear optimization method, for example, the potential field method, the probabilistic method, and so on. Although these methods are very powerful as calculation tools on a computer, their solutions are not optimal. We propose a novel method to calculate such an optimal path using a linear solution.