Q2) Consider the same problem as in P1. Assume that you now have access to a battery (electricity storage device) that can store 25 units of electricity. Running costs of the battery is negligible. In this variant of the problem, some of the production at hour h can be stored and serve the electricity demand at hour h+1. Formulate the problem to identify the production and electricity storage schedule that minimizes the cost of satisfying the demand.

Q3) Assume that the battery loses 5% of electricity it stores every hour. For example, if the battery has 30 units at hour h, it will have only 30*0.95=28.5 units of electricity at hour h+1. Which constraints would you change and how would you change them to model this new behavior?

[P1: 45pts] Consider a simple power network that has three power plants. The cost table and capacities for the power plants, along with the explanation of the metrics are provided below: Production cost indicates per unit electricity cost for the power plant. Commitment cost is the cost associated with keeping the power plant turned on. Note that to produce electricity, a plant needs to be committed (i.e. turned on). For instance, for Plant 3 to produce 30 units of electricity in the first hour, it first needs to be committed - which costs $100, and then needs to spend $(3018) on production of 30 units of electricity. Entire cost associated with electricity production would be $(100+3018)=$640. If a plant is committed, it can produce anywhere between its minimum committed capacity to its maximum committed capacity. Referring back to the example of Plant 3, if Plant 3 is committed (turned on), it can produce anywhere between 20 units and 50 units. Demands for the next 10 hours is listed below: Electricity cannot be stored without batteries. Therefore, for this problem, you can satisfy the demand at each hour with the production that occurred during the same hour. What would be the production schedule to minimize the cost associated with satisfying the demand in every hour