$2$pts$]$ Recall that in the basic Load Balancing Problem from Section $11\mathrm{.}1,$ were interested inplacing jobs on machines so as to minimize the makespan the maximum load on any onemachine. In a number of applications, it is natural to consider cases in which you have access tomachines with different amounts of processing power, so that a given job may complete morequickly on one of your machines than on another. The question then becomes: How should youallocate jobs to machines in these more heterogeneous systems? Heres a basic model thatexposes these issues. Suppose you have a system that consists of slow machines and fastmachines. The fast machines can perform twice as much work per unit time as the slowmachines. Now youre given a set of jobs; job takes time to process on a slow machine andtime $12$ to process on a fast machine. You want to assign each job to a machine; as before, thegoal is to minimize the makespanthat is the maximum, over all machines, of the totalprocessing time of jobs assigned to that machine. Give a polynomial$-$time algorithm thatproduces an assignment of jobs to machines with a makespan that is at most three times theoptimum