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Ch 4.4 Modeling and Optimization Graphical, Numerical, Algebraic by Finney Demana, Waits, Kennedy
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Example An open-top box is to be made by cutting congruent squares of side length x from the corners of a 20 by 25 inch sheet of tin and bending up the sides. How large should the squares be to make the box hold as much as possible? What is the maximum volume? x 25 20
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Example An open-top box is to be made by cutting congruent squares of side length x from the corners of a 20 by 25 inch sheet of tin and bending up the sides. How large should the squares be to make the box hold as much as possible? What is the maximum volume? x 25 20 + - 3.68 V '
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Example Find two numbers whose sum is 20 and whose product is as large as possible.
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Example Find two numbers whose sum is 20 and whose product is as large as possible. + - 10 P '
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Example What dimensions should a right cylinder containing a one liter of oil be that would use the least amount of material? (1 liter = 1000 cm3. r h
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Example What dimensions should a right cylinder containing a one liter of oil be that would use the least amount of material? (1 liter = 1000 cm3. r h
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