Consider the following scheduling problem. There are m machines, each of which can process jobs, one job at a time. The problem is to assign jobs to machines (each job needs to be assigned to exactly one machine) and order the jobs on machines so as to minimize a cost function. The machines run at different speeds, but jobs are identical in their processing needs. More formally, each machine i has a parameter li, and each job requires li time if assigned to machine i. There are n jobs. Jobs have identical processing needs but different levels of urgency. For each job j, we are given a cost function cj(t)that is the cost of completing job j at time t. We assume that the costs are nonnegative, and monotone in t. A schedule consists of an assignment of jobs to machines, and on each machine the schedule gives the order in which the jobs are done. The job assigned to machine i as the first job will complete at time li, the second job at time 21i and so on. For a schedule S, let tS(j) denote the completion time of job j in this schedule. The cost of the schedule is (S) = Σjcj(t(s)).

Required:
Give a polynomial-time algorithm to find a schedule of minimum cost.

Now you’re on your own. include a short summary of this section with plots in your lab report. write a matlab script file to do steps (a) through (d) below. include a listing of the script file with your report. 1 the soundsc(xx, fs) function requires two arguments: the first one (xx) contains the vector of data to be played, the second argument (fs) is the sampling rate for playing the samples. in addition, soundsc(xx, fs) does automatic scaling and then calls sound(xx, fs) to actually play the signal. mcclellan, schafer, and yoder, dsp first, 2e, isbn 0-13-065562-7. prentice hall, upper saddle river, nj 07458. c 2015 pearson education, inc. 4 mcclellan, schafer and yoder, signal processing first. prentice hall, upper saddle river, new jersey, 2003. c 2003 prentice hall. (a) generate a time vector (tt) to cover a range of t that will exhibit approximately two cycles of the 4000 hz sinusoids defined in the next part, part (b). use a definition for tt similar to part 2.2(d). if we use t to denote the period of the sinusoids, define the starting time of the vector tt to be equal to t , and the ending time as ct . then the two cycles will include t d 0. finally, make sure that you have at least 25 samples per period of the sinusoidal wave. in other words, when you use the colon operator to define the time vector, make the increment small enough to generate 25 samples per period. (b) generate two 4000 hz sinusoids with arbitrary amplitude and time-shift. x1.t / d a1 cos.2