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OPTIMIZATION PROBLEMS Section 3.7

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When you are done with your homework, you should be able to… Solve applied minimum and maximum problems

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Hypatia lived in 400AD. She was the most famous woman scientist of antiquity. How did she die? A.Giving birth. B.She was stoned to death and torn limb to limb by an angry mob of early Christians. C.She succumbed to the Black Plague. D.She was fatally injured when thrown from a horse.

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GUIDELINES FOR SOLVING APPLIED MINIMUM AND MAXIMUM PROBLEMS 1.Identify all given quantities and all quantities to be determined. MAKE A SKETCH!!! 2.Write a primary equation for the quantity that is to be maximized or minimized. 3.Reduce the primary equation to one having a single independent variable. You may need to use secondary equations relating the independent variables of the primary equation. 4.Determine the feasible domain of the primary equation. 5.Determine the desired maximum or minimum value using the techniques learned in 3.1-3.4.

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A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals. What dimensions should be used so that the enclosed area will be a maximum? GIVEN QUANTITIESQUANTITIES TO BE DETERMINED 200 FEET OF FENCING MAXIMUM AREA

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The primary equation will relate to the perimeter. A.True B.False

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STEP 2-3: FIND THE PRIMARY AND SECONDARY EQUATIONS.

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STEP 4. DETERMINE THE REASONABLE DOMAIN

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STEP 5. FIND MAXIMUM AREA

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An industrial tank is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 3000 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize cost.

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STEP 1. GIVEN QUANTITIESQUANTITIES TO BE DETERMINED TOTAL VOLUME IS _____CUBIC FEET MINIMUM __________ _______ GIVES US MINIMUM COST LET k = cost per square foot of the surface area of the sides and ___ = cost of the surface area of the ends

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STEP 2-3: FIND THE PRIMARY AND SECONDARY EQUATIONS.

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STEP 4. DETERMINE THE REASONABLE DOMAIN

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STEP 5. FIND MINIMUM COST

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