MAT135H1 Lecture 9: 3.3 Optimization Problems (3)

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Published on 22 Sep 2020
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3.3 Optimization Problems
Optimization is a procedure used in many fields to determine the best possible solution given a set of
restrictions
! Examples:
1) In engineering design (i.e. dimensions of design, cost of materials)
2) In economics (i.e. maximizing profits)
Algorithm for Solving Optimization Problems
1) Understand the problem and draw a diagram
2) Determine the quantity to be optimized
3) Create a function,
()
fx
, in one variable that represents the quantity to be optimized
[ex. dimension, price, number of units, etc]
4) Determine the domain (restrictions) of the function to be optimized
5) Use the algorithm from Section 3.2 to find the absolute maximum or minimum value in the domain
Example 1: There is 800 m of fencing available to enclose a rectangular field. One side of the field is facing a river and
does not require fencing. Determine the dimensions to enclose the maximum possible area using all of the fencing.
let x'np width
XXmaximize area
Alxw
800 2x a02x X
Domani
OLx 400 Atx 800 22
Hfu'd A'Cx
400
1Ax800 4x
bOSou 4
4X800
TF
121 200 7
at xno Ano 800 zoo zzoo
so 000 mMax area
oThe maximum area is 80000m2 with
dimension of 200 MXboom
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