Determine the schedule of unit commitment in a $4$ unit plant for a load of $6$MW$,$ if the load step is $1$MW$.$ The cost curves for four units are approximated as:

F$1=0\mathrm{.}35$P$12+25$P$1$ Rs$./$hr$.$ F$2=0\mathrm{.}8$P$22+27$P$2$ Rs$./$hr$.$

F$3=1\mathrm{.}1$P$32+30$P$3$ Rs$./$hr$.$ F$4=1\mathrm{.}2$P$42+33$P$1$ Rs$./$hr$.$

Neglect Transmission losses. Use Dynamic Programming technique.