Windsor Power can store power in a high-capacity battery. The battery has capacity to store 80 kWh (kilowatt hours). During a particular period, Windsor 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 The maximum rate that power can be injected or withdrawn from the battery is 20 kWh per period. Windsor has forecasted the following LMPs for the next 10 periods:

Develop and solve a linear programming model that will assist Windsor Power in determining how to best buy, store or sell electricity for the next 10 periods based on the LMP. Assume that the battery is half full at the beginning of period 1. That is, at the start of the planning horizon, the battery contains 40 kilowatt hours (kWh)
of electricity. It costs $1 to hold 1 kWh in the battery per period. Be sure to define all decision variables.

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Period LMP ($/kWh) 32 27 22 15 4 5 6 7 8 9 10 25 22 29 24 20 20 61 66