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Question: The company has one main generator that normally runs 24 hours a day and two (2) other secondary generators (i.e. Generator number 1 & 2) that provide additional power when needed. A start-up cost is incurred whenever a generator is started. The start-up costs are P2000 for 1 and P1500 for 2. These generators are used in the following ways: A generator may be started at 6:00 AM and run either for 8 hours or 16 hours, or it may be started at 2:00 PM and run for eight hours (until 10:00 PM).
Save for the main generators, all generators are shut down at 10:00 PM. Forecast indicate the need for 200 megawatts more than provided by the main generator after 6:00 AM and before 2:00 PM, and this need rises to 350 between 2:00 PM and 10:00 PM. Generator 1 may provide up to 250 megawatts per shift while generator 2 may provide up to 220 megawatts per. The cost per megawatt P35 is for Generator 1 and P40 for Generator 2. Formulate an ILP model that may be used to solve for the optimal cost for this power plant.
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