[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: Metric Metric Plant1 Plant2 Plant3 Type Descriptions Cost Production Cost (per unit) $30 $22 $18 Factors Commitment Cost $130 $100 $100 Capacity Maximum Committed Capacity (units) 20 30 50 Factors Minimum Committed Capacity (units) 5 10 20 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 $(30*18) on production of 30 units of electricity. Entire cost associated with electricity production would be $(100+30*18) = $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: 2 3 4 5 6 7 8 9 10 1 50 50 80 70 80 70 50 60 70 100 [P2:50 pts] 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