* This input file is an example for generating * integral solutions to the following system of linear inequalities: * 10 x1 + 7 x2 <= 70 * 11 x1 + 5 x2 >= 55 * x1 >= 0, x2 >= 0 * By using the fact that 0<=x1<=7 and 0<=x2<=10, we apply * the (binary representation) substitution: x1 = 4 x13 + 2 x12 + x11 (all binary variables) x2 = 8 x24 + 4 x23 + 2 x22 + x21 (all binary variables) * The reduced system of linear inequalities is the input data. * Since all integral (i.e. 0-1) solutions are extreme points, * the integral extreme points are in one-to-one correspondence * with the integral solutions to the original system. In this * example, there are 194 extreme points among which 10 are * integral (0-1) solutions. H-representation begin 16 8 integer 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 0 0 -1 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 -1 70 -40 -20 -10 -56 -28 -14 -7 -55 44 22 11 40 20 10 5 end