I require the solutions to the following TWO linear programming models with sensitivity reports using Excel Solver. Please attach Excel file after completed:

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 The maximum rate that power can be injected or withdrawn from the battery is 20 kWh per period.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:

A. Develop a linear programming model Star Power can 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?

Here is the linear program model: Let X_trepresent the amount to buy into period t, W_trepresent the amount to sell in period t, and I_t, represent the battery level at the end of period t.

Here is the model I created which I need solved:

Max 5 (W₁- X₁) + 27 (W₂- X₂) + 2 (W₃- X₃) + 25 (W₄- W₄) + 22 (W₅- X₅) + 29 (W₆- W₆) + 24 (W₇- W₇) + 20 (W₈- X₈) + 61 (W₉- W₉) + 66 (W₁₀- W₁₀)

I₁ X₁+ W₁= 60

I₂ I₁ X₂+ W₂= 0

I₃ I₂ X₃+ W₃= 0

I₄ I₃ X₄+ W₄= 0

I₅ I₄ X₅+ W₅= 0

I₆ I₅ X₆+ W₆= 0

I₇ I₆ X₇+ W₇= 0

I₈ I₇ X₈+ W₈= 0

I₉ I₈ X₉+ W₉= 0

I₁₀ I₉ X₁₀+ W₁₀= 0

X_t< 20

W_t<20

I_t<60

I₁= 60

X_t, W_t, I_t>0

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 (60 kWh) at the end of period 10. How does this impact the optimal profit?

Here is the model i created that needs to be solved:

Max 5 (W₁- X₁) + 27 (W₂- X₂) + 2 (W₃- X₃) + 25 (W₄- W₄) + 22 (W₅- X₅) + 29 (W₆- W₆) + 24 (W₇- W₇) + 20 (W₈- X₈) + 61 (W₉- W₉) + 66 (W₁₀- W₁₀)

I₁ X₁+ W₁= 60

I₂ I₁ X₂+ W₂= 0

I₃ I₂ X₃+ W₃= 0

I₄ I₃ X₄+ W₄= 0

I₅ I₄ X₅+ W₅= 0

I₆ I₅ X₆+ W₆= 0

I₇ I₆ X₇+ W₇= 0

I₈ I₇ X₈+ W₈= 0

I₉ I₈ X₉+ W₉= 0

I₁₀ I₉ X₁₀+ W₁₀= 0

X_t< 20

W_t<20

I_t<60

I₁= 60

I₁₀= 60

X_t, W_t, I_t>0