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a mortgage immediate programming graphical method of solution and the problem is maximize Z equals to minus X 1 plus 2 X 2 subject to X 1 minus X 2 less than or equal to minus 1 minus 0.5 X 1 plus X 2 less than or equal to 2 and X 1 and X 2 both are non-negative yes both the constraints are having negative signing them just beard okay as usual as I had explained in the previous case we are going to segregate all the constraints into two part equality to draw the straight line and an inequality to get the feasible region okay x1 minus x2 equals 2 minus 1 now we can have the two points to draw the straight line of this equation if x1 takes when you zero of that it will be minus x2 equals to minus 1 so x2 equals to 1 if it's 2 days when you zero that it will be x1 equals to minus 1 now if we start off in equality part of the same constraint x1 minus x2 less than minus 1 if x1 takes value 0 that it will be minus x2 less than minus 1 be error whenever there is negative sign in any of the s...