Formulate as a Linear Programming problem in standard form.

Power generators of four different types are available to satisfy the daily electricity demands (in megawatts) summarized in the following table. We consider a sliding time horizon: the period 10pm-12am of day d is followed by the period 0am-6am of day d + 1. Table 6.10: Daily electricity demands (in MW) Period 0am-6am 6am-9am 9am- 12pm- 2pm-6pm 6pm- 10pm- 12am 12pm 2pm 10pm demand 12000 32000 25000 36000 25000 30000 18000 The power generators of the same type have a maximum capacity and may be connected to the network starting from a certain minimal power output. They have a start-up cost, a fixed hourly cost for working at minimal power, and an hourly cost per additional megawatt for anything beyond the minimal output. These data are given in the following table. Table 6.11: Description of power generators Available Add. MW Start-up Min. output in MW Max. capacity in MW Fixed cost $/h number cost $/h cost Type 1 10 750 1750 2250 2.7 5000 Type 2 4 1000 1500 1800 2.2 1600 Type 3 8 1200 2000 3750 1.8 2400 Type 4 3 1800 3500 4800 3.8 1200 A power generator can only be started or stopped at the beginning of a time period. As opposed to the start, stopping a power plant does not cost anything. At any moment, the working power generators must be able to cope with an increase by 20% of the demand forecast. Which power generators should be used in every period in order to minimize the total daily cost? Power generators of four different types are available to satisfy the daily electricity demands (in megawatts) summarized in the following table. We consider a sliding time horizon: the period 10pm-12am of day d is followed by the period 0am-6am of day d + 1. Table 6.10: Daily electricity demands (in MW) Period 0am-6am 6am-9am 9am- 12pm- 2pm-6pm 6pm- 10pm- 12am 12pm 2pm 10pm demand 12000 32000 25000 36000 25000 30000 18000 The power generators of the same type have a maximum capacity and may be connected to the network starting from a certain minimal power output. They have a start-up cost, a fixed hourly cost for working at minimal power, and an hourly cost per additional megawatt for anything beyond the minimal output. These data are given in the following table. Table 6.11: Description of power generators Available Add. MW Start-up Min. output in MW Max. capacity in MW Fixed cost $/h number cost $/h cost Type 1 10 750 1750 2250 2.7 5000 Type 2 4 1000 1500 1800 2.2 1600 Type 3 8 1200 2000 3750 1.8 2400 Type 4 3 1800 3500 4800 3.8 1200 A power generator can only be started or stopped at the beginning of a time period. As opposed to the start, stopping a power plant does not cost anything. At any moment, the working power generators must be able to cope with an increase by 20% of the demand forecast. Which power generators should be used in every period in order to minimize the total daily cost