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1. Consider a company operating a hydropower plant. The plant consists of a reservoir (an artificial lake) created using a dam to store water. The water can be released from the reservoir through a series of pipes leading to a turbine, thereby producing electricity which is then sold on the electricity market. Let T be the planning period, consisting of |T| days. For each day t E T, let ft be the inflow, i.e., the total amount of water (in m') that enters the reservoir (due to, e.g., rivers flowing into it, snow melting in summer, rain, ...). Let the decision variable Xt, for each t ET, represent the amount of water (in m') that is released to produce energy. Let also Tt, for each t e T, be the amount of money (in pounds) made by selling on the electricity market the energy that is produced by releasing a m' of water at time tET. Formulate the problem of deciding how much water to release at each point in time so as to maximize the total revenue. Note that, at time t = 0, the reservoir contains a m of water and that, at time t = |T| it should contain at least 0.5 a. The maximum amount of water that can be stored is B, and the maximum amount that can be released at each point in time is 7