Optimization problem are all about realizing the best possible outcome in a situation, subject to a identify the absolute maximum or minimumAKAST SELE OUTCO derivative equ can can occur at the endpoints of an interval, or at points for which 1. Draw a diagram label variables and constants. 2. Define: Ovanables (with units) quantity to be maximized or minimized (with units). 3. Write a fonction for the quantity and define a closed interval for the function. 4. Differentiate the function. 3. Let dy - and solve Use PDT. 6. Find the y-coordinates for the endpoints of the interval value that make - Contical valves) 7. Therefore statemenil. Ex. 1 Three sides of a rectangular field fenced in with 400 m offencing. Find the dimensions x x Let x represent the width of the enclosure, in metres, x70 Lety represent the length of the enclosure, in metres, yoo. P=2x+y₁ 400=2x+y 400-2x=4 A= xy. Subin A= x(400-2x) = 400x-2x² dA όχι 400-47 set dA-O όχ 0=400-4 FDT 100 = x fox) fox) αA Interval Solh Ford ax 14100 + > x=100 N/A max. 07100 - <0 Sub x=100 to ①. y=400-2(100) = 00 the dimensions of the rectangle would be
Optimization problem are all about realizing the best possible outcome in a situation, subject to a identify the absolute maximum or minimumAKAST SELE OUTCO derivative equ can can occur at the endpoints of an interval, or at points for which 1. Draw a diagram label variables and constants. 2. Define: Ovanables (with units) quantity to be maximized or minimized (with units). 3. Write a fonction for the quantity and define a closed interval for the function. 4. Differentiate the function. 3. Let dy - and solve Use PDT. 6. Find the y-coordinates for the endpoints of the interval value that make - Contical valves) 7. Therefore statemenil. Ex. 1 Three sides of a rectangular field fenced in with 400 m offencing. Find the dimensions x x Let x represent the width of the enclosure, in metres, x70 Lety represent the length of the enclosure, in metres, yoo. P=2x+y₁ 400=2x+y 400-2x=4 A= xy. Subin A= x(400-2x) = 400x-2x² dA όχι 400-47 set dA-O όχ 0=400-4 FDT 100 = x fox) fox) αA Interval Solh Ford ax 14100 + > x=100 N/A max. 07100 - <0 Sub x=100 to ①. y=400-2(100) = 00 the dimensions of the rectangle would be
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.2: Graphs
Problem 15E
Question
in his model for storage and shipping costs for a manufacturing process, a researcher develops the following formula c=100(100+9x+144/x), where C is the most storage and transportation for up to 100 days of operation and load of material is moved every "x" days. Find the value of x for which C is a minimum.
(This is a calculus optimization problem, please show all work and add the chart for the first derivative test just like this example I am giving here, do the work like the example and put that chart too)
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