Many phenomena in life, engineering, science, and business finance require meeting an objective (optimal solution that has to be maximized or minimized) that can be represented by an objective function of the form P = Ax + By. This system has 2 variables. In real-life situations, the objective function is usually subject to at least one or more constraints and non-zero constraints expressed as inequalities w.r.t. to the variables in the objective function (known as decision variables). For up to 2 variables, these linear programming problems can be solved graphically. Typically, the constraints are plotted and the intercepts and intersection points of the constraints form the corner points of the feasible region. The feasible region as dictated by the intersection of the constraint inequalities can be a bounded region or an unbounded region. Usually, the optimal solution to the objective function, be it maximization or minimization, is found in the corner points, (x,y), which is a point on the graph of the objective function. When there are more than 2 variables with many more constraints, solving the problem graphically becomes tedious and complicated. Then, the Simplex Method is used to solve the problem algebraically.
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