Since there are only two variables , we can solve this problem using the Graphical Method by graphing the set of points in the plane that satisfies the constraint set and then finding which point of this set maximizes the value of the objective function . Each inequality constraint is satisfied by a half-plane of points, and the constraint set is the intersection of all the half-planes. In the present example, the constraint set is the five-sided figure shaded in Figure 1.(2)
We want to determine the point 〖( x〗_(1 ),x_█(2@)) that maximizes the objective function . The function 〖 x〗_(1 )+ x_█(2 @)is constant over any line with slope = -1 and as we move this line further up and to right from the origin the value of the function
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- The linear programming problem is feasible if the constraints set is not empty , otherwise it is infeasible . - The linear programming problem is said to be unbounded when the objective function is infinite , so it has a solution that can be made infinitely large without violating any of its constraints . All Linear Programming Problems Can be Converted to Standard Form All problems defined as maximizing or minimizing a linear function subjected to a linear constraints can be converted into the form of a standard maximum problem by the following techniques : (1) A minimum problem can be converted to standard maximum by multiplying the objective function by -1 . Also , constraints of the form ∑_(j=1)^(n )▒a_(ij ) x_j ≥ b_i can be changed to the form ∑_(j=1)^(n )▒〖-a〗_(ij ) x_j ≤- b_i . (2) Some constraints may be equalities An equality constraint (n j=1 aijxj = bi may be removed, by

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