1001_4.5_Lab_21 - 1 An open top box with a square base is...

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CALCULUS 1 LAB 21 NAME: ___________________PARTNER:_________________ 4.5 Applied Optimization Problems GSA:______________________Lab Time: ____________ Basic Guidelines: Step 1: Draw and label a figure appropriate for the problem. Step 2: Write down the equation that defines the quantity to be maximized or minimized. Step 3: If the equation is in terms of two variables, find a second equation so that the first equation can be put into terms of one variable. Step 4: Find the domain where the quantity is defined. (Is this an open or a closed interval?) Step 5: Check for absolute extrema of the quantity using ideas from 4.4, 4.3, and 4.2.
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Unformatted text preview: 1. An open top box with a square base is made from a square piece of cardboard by cutting out the corners and folding up the sides. If the dimensions of the cardboard are 9 inches by 9 inches, then what size cut will maximize the volume and what is the absolute maximum volume? 2. A cylindrical container, open at the top is to hold 512 = (8)(8)(8) cubic centimeters of water. Find the absolute minimum area and the height and radius that minimize the amount of material (area) needed to manufacture the container....
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