An electric utility currently operates ten plants. The following table gives the fixed costs, variable costs, and capacities of each of these plants. Daily demand is highly uncertain, given by a normal distribution with a mean of 200,000 kwh and a standard deviation of 40,000 kwh. The utility produces power using the cheapest plants it has to meet the demand each day. If demand exceeds its total capacity, it buys power on the open market at $15/kwh. The utility needs to determine which plants to keep open in the long term, given that it will choose the cost-minimizing plants to use to produce power each day.

a. If all ten plants are kept open, what is the total expected cost of meeting demand?
b. If the utility is allowed to close some plants, which ones should it close and what will be the resulting minimum cost

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Capacity (000 kwh) Fixed cost Variable cost ($/ kwh) ($000) Plant 122 4.3 25 185 5.6 34 95 6.7 19 4 118 7.8 23 121 12.0 14 135 4.1 16 103 4.9 8. 188 6.2 21 119 5.6 33 10 156 6.9 12