Mặc dù về cơ bản là một phần mở rộng của đại số tuyến tính được bảo hiểm trong cơ thể chính của chương này, các kỹ thuật lập trình tuyến tính liên quan đến tính năng đặc biệt mà phân biệt nó với các ứng dụng đại số tuyến tính khác. Khi tất cả các chức năng có liên quan tuyến tính, kỹ thuật này cho phép một: | Appendix linear programming Although basically an extension of the linear algebra covered in the main body of this chapter the technique of linear programming involves special features which distinguish it from other linear algebra applications. When all the relevant functions are linear this technique enables one to calculate the profit-maximizing output mix of a multi-product firm subject to restrictions on input availability or calculate the input mix that will minimize costs subject to minimum quality standards being met. This makes it an extremely useful tool for managerial decision-making. However it should be noted that from a pure economic theory viewpoint linear programming cannot make any general predictions about price or output for a large number of firms. Its usefulness lies in the realm of managerial or business economics where economic techniques can help an individual firm to make efficient decisions. Constrained maximization A resource allocation problem that a firm may encounter is how to decide on the product mix which will maximize profits when it has limited amounts of the various inputs required for the different products that it makes. The firm s objective is to maximize profit and so profit is what is known as the objective function . It tries to optimize this function subject to the constraint of limited input availability. This is why it is known as a constrained optimization problem. When both the objective function and the constraints can be expressed in a linear form then the technique of linear programming can be used to try to find a solution. Constrained optimization of non-linear functions is explained in Chapter 11. We shall restrict the analysis here to objective functions which have only two variables . when only two goods contribute to a firm s profit. This enables us to use graphical analysis to help find a solution as explained in the example below. Example A firm manufactures two goods A and B using three inputs K L .
