4 7 solving max min problems n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
4.7 Solving Max-Min Problems PowerPoint Presentation
Download Presentation
4.7 Solving Max-Min Problems

Loading in 2 Seconds...

play fullscreen
1 / 16

4.7 Solving Max-Min Problems - PowerPoint PPT Presentation


  • 56 Views
  • Uploaded on

4.7 Solving Max-Min Problems. Read 3 . Identify the known quantities and the unknowns. Use a variable. Identify the quantity to be optimized. Write a model for this quantity. Use appropriate formulas. This is the primary function.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '4.7 Solving Max-Min Problems' - salim


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
4 7 solving max min problems
4.7 Solving Max-Min Problems
  • Read3. Identify the known quantities and the unknowns. Use a variable.
  • Identify the quantity to be optimized. Write a model for this quantity. Use appropriate formulas. This is the primary function.
  • If too many variables are in the primary function write a secondary function and use it to eliminate extra variables.
  • Find the derivative of the primary function.
  • Set it equal to zero and solve.
  • Reread the problem and make sure you have answered the question.
slide2

An open box is to be made by cutting squares from the corner of a 12 by 12 inch sheet and bending up the sides. How large should the squares be cut to make the box hold as much as possible?

Figure 3.43: An open box made by cutting the corners from a square sheet of tin. (Example 1)

slide3

An open box is to be made by cutting squares from the corner of a 12 by 12 inch sheet and bending up the sides. How large should the squares be cut to make the box hold as much as possible?

Figure 3.43: An open box made by cutting the corners from a square sheet of tin. (Example 1)

Maximize the volume

V =l w h

V =(12 – 2x) (12 – 2x) x =144x – 48x2 + 4x3

V  = 144 – 96x+ 12x2 = 12(12 –8x+ x2)

12(12 –8x+ x2) = 0

(6-x)(2-x) = 0

x = 6 or x = 2

V  = -92+ 24x is negative at x = 2. There is a relative max. Box is 8 by 8 by 2 =128 in3.

minimizing surface area
Minimizing surface area

Figure 3.46: The graph of A = 2 r 2 + 2000/r is concave up.

You have been asked to design a 1 liter oil can in the shape of a right cylinder. What dimensions will use the least material?

slide5

Figure 3.46: The graph of A = 2 r 2 + 2000/r is concave up.

You have been asked to design a 1 liter oil (1 liter = 1000cm3) can in the shape of a right cylinder. What dimensions will use the least material?

Minimize surface area

where

Use the 2nd derivative test to show values give local minimums.

4 8 business terms
4.8 Business Terms

x = number of items

p = unit price

C = Total cost for x items

R = xp = revenue for x items

= average cost for x units

P = R – C or xp - C

slide7

The daily cost to manufacture x items is C = 5000 + 25x 2. How many items should manufactured to minimize the average daily cost.

14 items will

minimize the daily

average cost.

4 10 old problem
4.10 Old problem

Given a function, find its derivative

function

derivative

Inverse problem

Given the derivative, find thefunction.

.

slide9

Find a function that has a derivative y = 3x2

The answer is called the antiderivative

You can check your answer by differentiation

curves with a derivative of 3x 2
Curves with a derivative of 3x2

Each of these curves is

an antiderivative of y = 3x2

antiderivatives
Antiderivatives

Derivative

Antiderivative

find antiderivatives
Find antiderivatives

Check by differentiating

slide16

Derivative

Antiderivative