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Unformatted text preview: 1 Section 4.6 Optimization Problems • Goals – Apply our earlier work on maximum and minimum values to finding the optimum value of some variable. Steps For Optimization Problems • We can adapt the problem-solving principles discussed earlier to give these steps for solving optimization problems: 1. Understand the Problem Read the problem until it is clearly understood. Ask yourself: • What is the unknown? • What are the given quantities? • What are the given conditions? Steps For Optimization Problems 2. Draw a Diagram In most problems it is useful to draw a diagram and identify the given and required quantities on the diagram. 3. Introduce Notation Assign a symbol to the quantity that is to be maximized or minimized (let’s call it Q for now). Also select symbols ( a , b , c , …, x , y ) for other unknown quantities and label the diagram with these symbols. Steps For Optimization Problems 3. Notation (cont’d) It may help to use initials as suggestive symbols—for example, A for area, h for height, t for time. 4. Express Q in terms of some of the other symbols from Step 3. 5. If Q has been expressed as a function of more than one variable in Step 4… • use the given information to find relationships (in the form of equations) among these variables. 2 Steps For Optimization Problems 5. (cont’d) • Then use these equations to eliminate all but one of the variables in the expression for Q . • Thus, Q will be expressed as a function of one variable, say, Q = f(x ) . • Write the domain of this function. 6. Use the methods of Sections 4.2 and 4.3 to find the absolute maximum or minimum value of Q ....
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This note was uploaded on 04/18/2008 for the course MATH 210 taught by Professor Zhoramanseur during the Spring '08 term at SUNY Oswego.
- Spring '08