2311lectureoutline4.7

2311lectureoutline4.7 - any other unknown quantities. Label...

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MAC2311, Calculus I 4.7 Optimization Problems We will now apply what we’ve learned about finding extreme values to solve such practical problems as maximizing areas, volumes, and profits and minimizing distances, times, and costs. In solving such practical problems, the greatest challenge is often to convert the word problem into a mathematical optimization problem by setting up the function that is to be optimized. Here are some suggested steps to take in solving optimization problems. 1. Read the problem carefully to determine… What is unknown? What are the given quantities? What are the given conditions? 2. Draw a diagram (if possible) and identify the given and required quantities on the diagram. 3. Assign symbols to the quantity that is to be maximized or minimized and for
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Unformatted text preview: any other unknown quantities. Label the diagram with these symbols 4. Write an equation (Primary Equation) expressing the unknown quantity in terms of the other symbols. 5. If your unknown quantity has been expressed a s a function of more that one variable, use the given information to write another equation (Secondary Equation) showing the relationships between the variables. Substitute this secondary equation into the primary equation, so that the primary equation will be in terms of only one variable. 6. Now use the methods that we learned previously to find the absolute maximum or minimum value of the function. Try exercises 6, 12, 18, 24 on pages 328-329 in your text....
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This note was uploaded on 12/12/2011 for the course MAC 2311 taught by Professor Teague during the Spring '11 term at Santa Fe College.

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