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We use optimal control theory to determine the optimal rate of change in the subscription fee and the optimal ratio of ad space to the total web page space for a web content provider. An optimal solution is obtained using the maximum principle approach and the model predictive control approach. Numerical experiments show that it is preferable to use the first approach when the planning horizon is short and the second approach when the planning horizon is long
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Mejjouali et al. (2023) studied this question.
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