In a paging system, the page size is p and a program requires P pages. The last page in the program is 50 per cent full. Each page requires t locations in the main memory page table. Obtain an equation for the total amount of main memory required for the program and page table entry combined. Find the page size to give minimum memory requirements by differentiating the total memory requirement equation with respect to p, and equating the result to zero. Determine a suitable page size for a program of 128 Kbytes given four bytes per page entry.