i=1 A magnetic tape contains n programs of length 11, 12...... We know how often each program is used: a fraction p; of requests to load a program i, (1in). This implies that - Pi=1. Information is recorded along the tape at constant density, and the speed of the tape is also constant. Each time a program is loaded, the tape is rewound to the beginning. If the programs are held in the order i..... in, the average time required to load a program is, 71 T = cxpi, xlin] j=1 k=1 (1) where, the constant c depends on the recording density and the speed of the drive. Our objective is to minimize T. Consider the following: If the programs are stored in the order of the increasing values of l, will it minimize T? If the programs are stored in the order of the decreasing values of p., will it minimize T? If the programs are stored in the order of the decreasing values of (p;/4), will it minimize T"? For each of the above, if your answer is 'yes', then please provide an argument as to why you think it will minimize T. If 'no', please provide a counter-example.