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Linear programming is a useful analytical technique for managerial decision-making and used to determine the optimal solution to a decision problem. This technique is ideally suited to solving decision problems that involve an objective to maximized or minimized. It is particularly powerful for the decision maker in solving business problems when constrains limit or restrict such as in the area of production related decisions, firms are often faced with a variety of capacity limitations. Limited availability of skilled labor, raw materials and so on, can all constrain production.
When such capacity constraints exist, managers must exercise careful judgment to insure that scarce resources are used in the most efficient manner possible to produce only the products that provide the greatest returns or profits.
Although linear programming is a valuable tool for solving maximization or minimization problems, it still has certain disadvantages. In the term of the linear programming cannot be used in the following three situations; First, if the strong economies of scale exist; second as the firm expands output, the prices of variable factors of production increase; and as output increases, product prices declines.
Why we cannot use the linear programming during those situations? That is because in the linear programming, the none-linear and discontinued is not allowed. As the assumption of linearity is based on considering the revenue function, production function and the profit function of the business must be linear. When output increase, revenues, costs and profits must increase linearly. And also for revenues to increase linearly with output, product prices must constant.
In general that in many instances the linearity assumptions are valid, and in other cases, when the assumption does not hold precisely, linear approximations will not seriously misrepresent the analysis.
Here I use a simple example and solve it with both graphic solution and tableau form, in order to described and explain the advantages and disadvantages of linear programming as a management aid.
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