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Question 1: Modelling in Linear Programming The manager of a power station has to determine an operating policy for next week's power genera-tion. The station has been scheduled to generate a total of 100 gigawatt hours of power during the next week. However, in accordance with the law, the manager has to carefully manage the power station's operating policy to control the emissions from the station. These emissions include particu-lates, carbon dioxide, and sulphur.

No more than 111kg of particulate emissions, 102kg of carbon dioxide, or 136kg of sulphur emissions may be produced per week. The power station can burn any combination of three possible fuels:

high grade (Grade A) coal, low grade (Grade B) coal, or gas. Grade A coal costs $2,600 per kiloton, Grade B coal costs $1,400 per kiloton, while gas costs $3,700 per kilojoule.

Burning 1 kiloton of grade A coal produces 0.72 giga-watt hours of power, 1 kiloton of grade B coal produces 0.67 gigawatt hours when burned, while gas produces 0.83 gigawatt hours per kilojoule burned. Political considerations require that at least 29% of the energy produced be generated from coal irrespective of grade. The emissions produced when a fuel is burned are given in Table 2 below: Grade A Coal (1 kiloton) Grade B Coal (1 kiloton) Gas (1 kilojoule) Particulates 1.2 kg 1.3 kg 1.0 kg Carbon dioxide 0.8 kg 1.3 kg 0.7 kg Sulphur 1.4 kg 1.5 kg 0.8 kg Table 1: Emissions...