As part of the hydraulic design of a pump $-$ pipeline system, the optimal pump characteristic curve needs to be determined by finding the values of P$1,$ P$2$ and P$3$ that satisfy the function

P$1-$ P$2\backslash$times $60$P$3=60.$

Table Q$5$ shows the initial randomly generated population $($of $6$ members$)$ of possible solutions to the

problem. Carry out one generation of genetic algorithm $($GA$)$ optimization using this initial population. Use a tournament size of $2$ and exclude mutation and elitism. Carry out two tests that would inform

you whether the GA si working as you would expect ti to$.$ Table Q$5$