Multiplatform advertising (MPA) is recognized as an effective means of enhancing marketing revenue. In the context, we refer to the scheme of dynamically allocating the advertising expenditure among the selected media platforms as an MPA policy, and we refer to the problem of developing an MPA policy with maximum benefit as the MPA problem. This article is devoted to the solution of the MPA problem. An evolutionary model for the expected market state, in which the influence of both advertising and word-of-mouth (WOM) propagation is accounted for, is established. On this basis, the expected benefit of an MPA policy is calculated. Thereby, the MPA problem is reduced to an optimal control problem we refer to as the MPA model, where the objective functional stands for the expected benefit of an MPA strategy. The optimality system for the MPA model is derived. We refer to the MPA policy obtained by solving the optimality system as the promising MPA policy. The structure of the promising MPA policy is inspected. Through extensive comparative experiments, it is concluded that the promising MPA policy is superior to the majority of MPA policies in terms of expected benefit. Finally, how the expected benefit of the promising MPA policy is influenced by some factors is investigated.