PLEASE ANSWER ASAP!!Problem 1. Suppose that we need to allocate one unit of power to two communication channels.The variable xi represents the transmitter power allocated to the ii=1,2ln(ai+xi) gives the communication rate of the channel i where ai>0,i=1,2ln(x)is the natural log with derivative {:(ln(x))'=1x).(1) Formulate anNLPPto determine the best power allocation to maximize the totalcommunication rate. (2 points)(2) List all KKT conditions for this NLPP.(Youdo not need to solve it.)(2 points)(3) Are the KKT conditions sufficient for a point tobe a global optimum for this problem?Justify your answer explicitly. (1 point) Problem 2. Lieutenant Electric owns a pumped hydroelectric plant, which consists of tworeservoirs-one above the other-and a turbine and pump. During each hour, the plant doesexactly one of the following things: (i) operate the turbine, (ii) operate the pump, or(iii)donothing. Ifit operates the turbine, it releases 1 unit of water from the upper reservoir andproduces 0.8MWhof electricity that can be sold in the wholesale market. Ifit operates thepump, it consumes 1MWhof electricity, which is purchased from the wholesale market, andpumps 1 unit of water into the upper reservoir. Ifit does nothing, the water level of the upperreservoir remains the same. The upper reservoir can hold at most 2 units of water, has 1 unit ofwater initasof the beginning of hour 1, and there are nolimitson the water level of the lowerreservoir. The wholesale price of electricity over the next 3 hours are:(1) Formulate a dynamic optimization problem to determine the profit-maximizing operationof the plant in the next 3 hours by identifying explicitly the problem's: (2 points)i. Decision stages,ii. Decision variables,iii. State variables,iv. State-transition functions,v. Constraints, andvi. Objective-contribution functions.(2) Use dynamic programming algorithm to solve the problem formulated in(1).i. Fill-in the tables (backward recursion).(2 points)ii. Recover an optimal solution (forward recursion)by answering the followingquestions: (a) What is the optimal objective value? (b) What is the optimalsequence of decisions? (1 point)