Optimization Problems

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# Optimization Problems - PowerPoint PPT Presentation

Optimization Problems. Lesson 4.7. Applying Our Concepts. We know about max and min … Now how can we use those principles?. Optimization Strategy. Note Guidelines, pg 260 from text. When appropriate, draw a picture Focus on quantity to be optimized

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## Optimization Problems

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### OptimizationProblems

Lesson 4.7

Applying Our Concepts
• We know aboutmax and min …
• Now how can we use thoseprinciples?
Optimization Strategy

Note Guidelines, pg 260 from text.

• When appropriate, draw a picture
• Focus on quantity to be optimized
• Determine formula involving that quantity
• Solve for the variable of the quantity to be optimized
• Find practical domain for that variable
• Use methods of calculus (min/max strategies) to obtain required optimal value
• Check if resulting answer “makes sense”
Example: Maximize Volume
• Consider construction of open topped box from single piece of cardboard
• Cut squares out of corners

60”

30”

What size squares to maximize the volume?

Small corner squares

Large corner squares

Use the Strategy
• What is the quantity to be optimized?
• The volume
• What are the measurements (in terms of x)?
• What is the variable which will manipulated to determine the optimum volume?
• Now use calculus principles

60”

x

30”

Minimize Cost
• We are laying cable
• Underground costs \$10 per ft
• Underwater costs \$15 per ft
• How should we lay the cable to minimize to cost
• From the power station to the island

Power Station

500

2300

View example of a dog who seemed to know this principle

Use the Strategy

• Determine a formula for the cost
• \$10 * length of land cable + \$15 * length of under water cable
• Determine a variable to manipulate which determines the cost
• What are the dimensions in terms of this x
• Use calculus methods to minimize cost

Power Station

500

2300

Optimizing an Angle of Observation
• Bottom of an 8 ft high mural is 13 ft above ground
• Lens of camera is 4 ft above ground
• How far from the wallshould the camera be placed to photographthe mural with theLargest possible angle?

8

13

4

?

Try Animated

Demo

Assignment A
• Lesson 4.7A
• Page 265
• Exercises 1 – 35 odd

More examples from another teacher's website

Elvis Fetches the Tennis Ball
• Let r be therunning velocity
• Let s be theswimming velocity
• Find equation ofTime as function of y

z

Elvis Fetches the Tennis Ball
• Find T'(x)
• Set equal to zero
• Find optimum y
Elvis Fetches the Tennis Ball
• Determine Elvis's quickness
• Running
• Swimming
• Average 3 fastest
• r = 6.4 m/s
• s = .910 m/s
• Plug into optimum equation
Elvis Fetches the Tennis Ball
• r = 6.4 m/s
• s = .910 m/s
Elvis Fetches the Tennis Ball
• With graph of optimum function
Assignment B
• Lesson 4.7 B
• Page 268
• Exercises 43, 47, 54, 55, 58, 59, 60