4. Consider the travelling salesperson problem with 5 cities: A, B, C, D, E. You start in A and must visit each city exactly once before flying (directly) back to A. The cost of a one-way flight between pairs of cities (in hundreds of dollars) is given below (note: the cost to fly in either direction is the same for the purposes of this question).

AB(3), AC(2), AD(12), AE(7), BC(4), BD(9), BE(8), CD(7), CE(6), DE(6)

i. Using the greedy algorithm (at each step, taking the cheapest available flight to an unvisited city), what is the sequence of cities visited and what is the total cost of all flights taken?

ii. Is the solution from part i optimal? If it is, explain how you know it is. If not, find a solution that is optimal.