solve complete

Exercise 2 You are tasked with shipping a number n of goods gi {1,...,n} to a target location ti. In your very rural area, the roads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies you can use for the transport of any good gi. You have to order one truck for each good, and know the companies' routes Pi,1, P1,2 and Pi,3 they would take to all specific locations, where each route consists of a sequence of road segments that it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transports to be obstructed, your aim is to pick the paths Pij for each good in such a way that max{Zeep., 1le E} is as small as possible. (a) Formulate the problem as an ILP, and relax to an according LP. (b) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees a 3- approximation to the optimal solution, and prove its approximation guarantee