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5 steps to follow under graphical solution to a linear programming

steps to be followed under graphical solution to a linear programming problem.

Step1. Determine the region that satisfies the set of given inequalities.

Step 2. Ensure that the region is bounded*. If the region is not bounded, either there are additional hidden conditions which can be used to bound the region or there is no solution to the problem.

Step 3. Construct the matrix E of the extreme points, and the column vector C of the objective function.

Step 4. Find the matrix product EC. For maximization, determine the row in EC where the largest element appears; while for minimization, determine the row in EC where the smallest element appears.

Step 5. The objective function is optimized corresponding to the same row elements of the extreme point matrix E.

If the slope of the objective function be same as that of one side of feasible region, there are multiple solutions to the problem. However, the optimized value of the objective function remains the same.
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