2.Problem (Nonlinear model): Network Flow Problem Safety Trans is a trucking company that specializes transporting extremely valuable and extremely hazardous materials. Due to the nature of the business, the company places great importance on maintaining a clean driving safety record. This not only helps keep their reputation up but also helps keep their insurance premium down. The company is also conscious of the fact that when carrying hazardous materials, the environmental consequences of even a minor accident could be disastrous. Safety Trans likes to ensure that it selects routes that are least likely to result in an accident. The company is currently trying to identify the safest routes for carrying a load of hazardous materials from Los Angeles to Amarillo, Texas. The following network summarizes the routes under consideration. The numbers on each arc represent the probability of having an accident on each potential leg of the journey. Flagstaff Albuquerque 0.006 0.001 Las Vegas 6 8 2 0.001 0.003 Amarillo Los Angeles 0.010 0.006 10 0.002 0.010 0.004 0.009 0.006 0.004 0.002 0.005 0.002 Phoenix 9 3 5 7 0.003 San Diego 0.010 Lubbock Tucson 0.003 Las Cruces The objective is to find the route that minimizes the probability of having an accident, or equivalently, the route that maximizes the probability of not having an accident.Some help for this problem Creating the mathematical model to represent the problem:| Each decision variable indicates whether or not a particular route is taken (they are known as binary variables). We will dene these variables in following way: Xi] = 1 , if the route from node i to nodej is selected, and Xi] = 0 otherwise. Let Pij be the probability of having an accident while travelling from node i to node j (1- Pij is the probability of not having an accident). Objective function: Minimize the probability of having an accident or equivalently, maximize the probability of not having an accident. Note that this objective function is nonlinear. Maximize f(X12, X13,....) = (1-P12*X12) (1-P13*X13) (1 P14*X14) (1 P24*X24) .......... (1 - P9.10*X9,1o) Constraints are a little tricky. You will need to define binary constraints for the routes not taken. Set up the spreadsheet so that each node is an element (row) and define a cell that indicates if the route is taken or not. Those are the cells that are changes and in addition they are a constraint in that they need to be binary (taken, not Taken) shown as a 1 or a 0. In excel that is the cell reference set to 0. For Example: "ASlS:A$20$ = binary\" would go in the constraint line