1. Formulate the following as optimization problems, giving in each case a description of the set of feasible solutions F and the objective function c. Create a small instance for each problem, and state F and c. (a) Find the longest path in between any two nodes in a graph. (b) Find a cylinder with a given surface area A that has the largest volume. (c) Find a path on a graph that visits every node of the graph exactly once. (d) Given an nn chessboard, find the maximum number of rooks that can be placed such that none of them can attack to eachother