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4.7 Optimization Problems (with worked examples)

Notes
Course

Calculus & Analytic Geom I (MATH 109)

21 Documents
Students shared 21 documents in this course
Academic year: 2022/2023
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University of San Francisco

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4 Optimization Problems Optimization problems ask: What is the maximum (minimum) value of an objective function subject to the given constraints? Example 1:

É É

10 P 5 5 20 20 P 2 2 50150 coz t

PI

ko so P 2wt2L objective minimise Perimeter P 2wt2l constraint area is 100 A 100 we too P

2wt

W E P 2005 t 2L

P 200 L 2 t 2 0 looking for critical numbers 2 2 2 0 2 272 242 200 3 100 L I to Is 1 10 a minimum or maximum P 400 L 3 4 3 P 10 4 3 positive Perimeter is concare up at a 10 At the minimum perimeter since area is coo w

Example 3:

25 2 gg

mize

5610

25 1 2 27 5 10

h 1st number

m 2nd number If

objective

minimize sumn S ntm

constraint product so nm 50

sit In

E

S 51m m minimize

5 50m tm

s som't I o

critical numbers

9ft

1

I

E

m

2

50

M Wo 5F

s too m

3 3

s Bo

Eg

positive

S is concave

up

when M Fo

W minium use constraint to find n nm so n Tso 50 n roo as

####### 58

5

n F0 M Go

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4.7 Optimization Problems (with worked examples)

Course: Calculus & Analytic Geom I (MATH 109)

21 Documents
Students shared 21 documents in this course

University: University of San Francisco

Was this document helpful?
4.7 Optimization Problems
Optimization problems ask: What is the maximum (minimum) value of an objective function subject to the
given constraints?
Example 1:
ÉÉ
10 P5520 20 P2250150
coz
t
PI ko so P2wt2L
objective minimise Perimeter P2wt2l
constraint area is 100 A100 we too
P2wt2 WE
P2005 t2L

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