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21. Star Power Company is a power company in the Midwest region of the United States. Star buys and sells energy on the spot market. Star can store power in a high-capacity battery that can store up to 60 kWh (kilowatt hours). During a particular period, Star can buy or sell electricity at the market price known as LMP (Locational Marginal Price). The maximum rate that power can be injected or withdrawn from the battery is 20 kWh per period. Star has forecasted the following LMPs for the next 10 periods: Period LMP ($/kWh) $ 5 $27 $ 2$25 ovouw- $22 $29 $24 $20 $61 $66 The battery is full at the beginning of period 1; that is, at the start of theplanning horizon, the battery contains 60 kWh of electricity. a. Develop a linear programming model Star Powercan use to determine when to buy and sell electricity in order to maximize profit over these 10 weeks. What is the maxi- mum achievable profit? b. Your solution to part (a) should result in a battery level of 0 at the end of period 10. Why does this make sense? Modify your model with the requirement that the battery should be full

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