Outline the Kuhn-Tucker conditions, and the nature of problems for which they are relevant. Consider the following input-output characteristics for four thermal generating units: Unit 1 Unit 2 Unit 3 Unit 4 Pmin.1 = 200 MW Pmax.1 375 MW F = 11,000+ 13.2 P +0.08 P /h Reserve = min (Pmax.1- P, 0.25 Pmax.1) MW Pmin.2 = 80 MW Pmax2 250 MW F = 18,000 18.4 P + 0.13 P /h Reserve, min (Pmax2-P, 0.30 Pmax) MW - Pmin,3 155 MW Pmax.3 360 MW F3 = 22,050 - 25.6 P + 0.12 P /h Reserves = min (Pmax.s-P3, 0.28 Pmax 3) MW Pmin,4 = 300 MW Pmax4 365 MW F = 12,500 + 11.3 P4 +0.06 P /h Reserve. = min (Pmax.4-P4, 0.20 Pmax.4) MW Determine the optimal dispatch, and the associated cost, for these four units for a system demand of 970 MW, assuming that there is not a reserve requirement. What is the incremental cost of providing one additional MWh of energy? If sufficient reserve must now be carried to cover the loss of any single infeed, and the load can provide 40 MW of reserve, determine the optimal dispatch and the associated cost. What is the incremental cost of providing one additional MWh of energy, and, separately, what is the incremental cost of providing one additional MW of reserve?