Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are
$${\rm I}{C_1} = 20 + 0.3\,\,{P_1},\,{\rm I}{C_2} = 30 + 0.4\,\,{P_2},\,{\rm I}{C_3} = 30$$
Assume that all the three units are operating all the time. Minimum and maximum loads on each unit are $$50$$ $$MW$$ and $$300$$ $$MW$$ respectively. If the plant is operating on economic load dispatch to supply the total power demand of $$700$$ $$MW$$, the power generated by each unit is

The incremental cost characteristic of two generators delivering $$200$$ $$MW$$ are as follows $$\,\,\,{{d{F_1}} \over {d{P_1}}} = 20 + 0.1{P_1},\,\,{{d{F_2}} \over {d{P_2}}} = 16 + 0.2{P_2}$$
For economic operation, the generations $${P_1}$$ and $${P_2}$$ should be

An industrial consumer has a daily load pattern of $$2000$$ $$kW$$, $$0.8$$ lag for $$12$$ Hrs. and $$1000$$ $$kW$$ $$UPF$$ for $$12$$ Hrs. The load factor is