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