ABSTRACT
This chapter introduces the Lagrange Multipliers Method for finding the extrema of functions subject to certain constraints. The method is further applied to various settings such as: finding extrema of functions defined on compact sets, derive various inequalities involving real numbers, modelling problems in business and economics. The Lagrange Multipliers Method can be used to prove some important inequalities in algebra and trigonometry. In Economics, utility functions are used to describe consumers' relative preference for two or more goods or services. One simple example is the preference for certain types of foods, clothes or internet providers. In utility function problems the Lagrange multiplier is called the marginal utility of money.
