# Linear Programming

It is evidently clear from the discussion that since resources are scarce there are limitations on what can be achieved for example if materials and machine time are in short supply. Output, therefore, will be limited by the availability of these resources. It is a Constrained Optimization Problems arise from applications in which there are explicit constraints on the variables. The constraints on the variables can vary widely from simple bounds to systems of equalities and inequalities that model complex relationships among the variables. Constrained optimization problems can be furthered classified according to the nature of the constraints, for example, it can either be a linear, or nonlinear problem. The graph is in the first quadrant (W gt. 1, R gt.1) by virtue of the non-negativity constraints. The horizontal axis is assigned for W and R is assigned to the vertical axis. a coordinate is the ordered pair (W, R). At point A the revenue realized is at maximum thus is the best point of production the profit generated is at maximum. All the constraints are within range at this point thus it is the corner containing the optimal solution. An optimum point of production is the point where the units produced will yield the maximum profit within the limitations by the constraint. In this case at point A, the total profit that can be realized is \$124,500 this is the highest possible profit. To produce these profits we require 7 batches of valley wine White and 4.5 batches of valley wine Red. This means a total of 7,000 white wines and 4,500 Red wines. The corner point evaluation method is used to determine the corner that would generate the most profits or maximize the objective function. In this method, we take the all the corners coordinates and plug them in the objective and determine it which corner will maximize profit.