operations research problem

2. PECO needs to make plans for the energy systems for a new building. The energy needs in the building fall into three categories: 1)electricity, 2)heating water and 3)heating space in the building. The daily requirements for these three are: Electricity: 20 units Water Heating: 10 units Space Heating: 30 units. There are three possible sources of energy: electricity, natural gas and a solar heating unit that can be installed on the roof. The size of the roof limits the largest possible solar heater to 30 units but electricity and water heating have no limit. Electricity needs can only be met by purchasing electricity (at $50 per unit). Both other sources can be met by any source or combination of sources. The unit costs are (in %): Electricity Water heating $90 Space heating 80 Natural gas 60 50 Solar heater 30 40 a) Formulate the mathematical model to minimize cost b) Use the Northwest corner rule to solve this (showing steps). c) Compare your answer in part b to an optimal solution obtained from Excel