Stevens is considering installing solar energy systems to some of its buildings. The energy generation capacity...

 

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Stevens is considering installing solar energy systems to some of its buildings. The energy generation capacity and the energy demand fluctuate significantly from season to season. The university can store solar energy in battery systems to use it in later seasons where the demand is high. The storage cost is $10 per season per kWh. Energy used in the same quarter that it was generated does not incur any storage cost. In addition, the solar panels must be maintained regularly. The maintenance cost depends on the season and how much energy is generated from the system. The supply, demand and maintenance costs are given below: Demand (kWh) Supply (kWh) Maint. Cost ($/kWh) 25 Season Summer 22 Fall'22 Winter 23 Spring 23 Use the information above for the following a) [30pt] Formulate the linear programming problem of meeting the energy demand for these four seasons at minimum cost as a balanced transportation problem. Report the transportation tableau. 50 200 300 450 700 250 50 200 35 40 30 b) [25pt] Solve the balanced transportation problem from part a). Report a screenshot from your optimal solution and describe this solution verbally to tell how much energy should be generated in each season and when this energy will be used as well as the final cost at the optimum. - E.g., In the summer season X kWh of energy must be generated, Y kWh will be used in summer, Z kWh will be used in Fall etc. c) [15pt] You should see 200kWh of unused supply at the optimum. If Stevens had the option to sell this unused energy directly to the city of Hoboken (without storing them in battery), what is the minimum price that Stevens should charge the city of Hoboken in total for this 200kWh of solar energy? Show your work. Stevens is considering installing solar energy systems to some of its buildings. The energy generation capacity and the energy demand fluctuate significantly from season to season. The university can store solar energy in battery systems to use it in later seasons where the demand is high. The storage cost is $10 per season per kWh. Energy used in the same quarter that it was generated does not incur any storage cost. In addition, the solar panels must be maintained regularly. The maintenance cost depends on the season and how much energy is generated from the system. The supply, demand and maintenance costs are given below: Demand (kWh) Supply (kWh) Maint. Cost ($/kWh) 25 Season Summer 22 Fall'22 Winter 23 Spring 23 Use the information above for the following a) [30pt] Formulate the linear programming problem of meeting the energy demand for these four seasons at minimum cost as a balanced transportation problem. Report the transportation tableau. 50 200 300 450 700 250 50 200 35 40 30 b) [25pt] Solve the balanced transportation problem from part a). Report a screenshot from your optimal solution and describe this solution verbally to tell how much energy should be generated in each season and when this energy will be used as well as the final cost at the optimum. - E.g., In the summer season X kWh of energy must be generated, Y kWh will be used in summer, Z kWh will be used in Fall etc. c) [15pt] You should see 200kWh of unused supply at the optimum. If Stevens had the option to sell this unused energy directly to the city of Hoboken (without storing them in battery), what is the minimum price that Stevens should charge the city of Hoboken in total for this 200kWh of solar energy? Show your work.

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ANSWER a The linear programming problem of meeting the energy demand for these four seasons at minim... View the full answer