MATH-M 211 Lecture Notes - Lecture 16: Minimax
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Looking for greatest profit, least cost, least time, greatest voltage, optimum sizes, greatest strength, greatest distance, etc. Reduce primary equation to 1 single independent variable- may involve use of secondary equation relating independent variables of primary equation. Determine desired max/min value by techniques from sections 3. 1 to 3. 4. A standard beverage can is a right cylinder with volume 355 ml. Rebuild the can to hold the same volume using the least amount of material. (stay cylindrical, assume can was cylindrical to begin with) Sa = 2 circles + rectangle = 2 r2 + 2 rh. Need to make equation 1 variable- use known volume. Using a sheet of 8. 5 by 11 paper, find the optimum dimensions of an open box with maximum volume that can be made by cutting identical squares from each corner and folding up the sides. V = lwh h = x l = 11 2x. Critical numbers: x = 1. 585, x = 4. 915 (not in domain)
