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We demonstrate with a newspaper example in Japan that a large class of problems can be solves exactly by decomposing the objective function of the original problem into separable objective functions, and reformulate the problem into a multiobjective nonlinear knapsack problem, which is solved by a special algorithm called HOPE (Hybrid Optimization Process Equipment) within a practical time. The exact algorithm achieves improvement of the efficiency of media plan and provides many practical implications for media planners/advertisers as well as for media companies. For instance, the optimal combination of newspaper vehicles sometimes changes dramatically against a small change of budget. For media companies, this implies a chance of wining a majority of budget by offering a package of vehicles with an appropriate pricing.