lect116_20rev_f11 - Friday, October 28 Lecture 20 :...

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Friday, October 28 Lecture 20 : Optimization problems (Refers to Section 4.7 in your text) Students who have mastered the content of this lecture know about : Optimization problem and how they relate to absolute max and min of a function. Students who have practiced the techniques presented in this lecture will be able to : Solve various optimization problems. Introduction – Finding « extreme values » of functions is a procedure which will help solve certain types of problems encountered in everyday situations. We will study these types of problems here, practice interpreting them using mathematical language, and use our mathematical skills to answer questions related to the described situations. The problems we will discuss are known as “ optimization problems ”. They are sometimes referred to as “ max-min problems ”. 20.1 Steps in solving optimization problems. 1) Read the problem carefully asking yourself “what are the unkowns?”, “What is the quantity we want to maximize or minimize?”, “What are the given conditions or constraints?” 2) Draw a diagram, if possible, illustrating the quantities to maximize or minimize. 3) Introduce notation, to simplify your expressions. For example, m for mass, for velocity, A for area and so on. 4) Express quantities Q in terms of other variables using the notation introduced in step three. 5) If a quantity Q is expressed in terms of more than one variable, see if there are other equations which will allow you to express Q as a function of a single variable. 6)
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lect116_20rev_f11 - Friday, October 28 Lecture 20 :...

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