Deterministic Optimization

I hope this is clear.

(P6) A hydropower operator determines how much to produce each day based on the price of electricity and the water levels in the reservoir. Since hydropower plants need water to produce electricity, how much electricity a hydropower plant can produce is a function of the water levels in its reservoir. Given adequate water level, hydropower plant can produce up to 300 units of electricity per hour. However, if the water levels are not enough, full capacity cannot be used. (For instance, if there is enough water for 250 units of electricity in the reservoir, power plan can produce only 250 units). Assume that the current reservoir levels are enough for 250 units of electricity. The production cost for the power plant is 16.0$ per unit of energy. To produce electricity, power plant needs to be turned on. The cost associated with turning on the power plant is 250$ per hour. Power plant can sell produced electricity for 21.19$/hour. ) a) For a power plant that wants to maximize profit, formulate the problem for single period (single hour). Clearly define your variables, and parameters. No need to solve, only formulate. (20 pts) (P6) A hydropower operator determines how much to produce each day based on the price of electricity and the water levels in the reservoir. Since hydropower plants need water to produce electricity, how much electricity a hydropower plant can produce is a function of the water levels in its reservoir. Given adequate water level, hydropower plant can produce up to 300 units of electricity per hour. However, if the water levels are not enough, full capacity cannot be used. (For instance, if there is enough water for 250 units of electricity in the reservoir, power plan can produce only 250 units). Assume that the current reservoir levels are enough for 250 units of electricity. The production cost for the power plant is 16.05 per unit of energy. To produce electricity, power plant needs to be turned on. The cost associated with turning on the power plant is 250$ per hour. Power plant can sell produced electricity for 21.19$/hour. (10 points) a) For a power plant that wants to maximize profit, formulate the problem for single period (single hour). Clearly define your variables, and parameters. No need to solve, only formulate (P6) A hydropower operator determines how much to produce each day based on the price of electricity and the water levels in the reservoir. Since hydropower plants need water to produce electricity, how much electricity a hydropower plant can produce is a function of the water levels in its reservoir. Given adequate water level, hydropower plant can produce up to 300 units of electricity per hour. However, if the water levels are not enough, full capacity cannot be used. (For instance, if there is enough water for 250 units of electricity in the reservoir, power plan can produce only 250 units). Assume that the current reservoir levels are enough for 250 units of electricity. The production cost for the power plant is 16.0$ per unit of energy. To produce electricity, power plant needs to be turned on. The cost associated with turning on the power plant is 250$ per hour. Power plant can sell produced electricity for 21.19$/hour. ) a) For a power plant that wants to maximize profit, formulate the problem for single period (single hour). Clearly define your variables, and parameters. No need to solve, only formulate. (20 pts) (P6) A hydropower operator determines how much to produce each day based on the price of electricity and the water levels in the reservoir. Since hydropower plants need water to produce electricity, how much electricity a hydropower plant can produce is a function of the water levels in its reservoir. Given adequate water level, hydropower plant can produce up to 300 units of electricity per hour. However, if the water levels are not enough, full capacity cannot be used. (For instance, if there is enough water for 250 units of electricity in the reservoir, power plan can produce only 250 units). Assume that the current reservoir levels are enough for 250 units of electricity. The production cost for the power plant is 16.05 per unit of energy. To produce electricity, power plant needs to be turned on. The cost associated with turning on the power plant is 250$ per hour. Power plant can sell produced electricity for 21.19$/hour. (10 points) a) For a power plant that wants to maximize profit, formulate the problem for single period (single hour). Clearly define your variables, and parameters. No need to solve, only formulate