7. Applied Maximum and Minimum Problems

by M. Bourne

 

The process of finding maximum or minimum values is called optimisation. We are trying to do things like maximise the profit in a company, or minimise the costs, or find the least amount of material to make a particular object.

These are very important in the world of industry.

 

Example 1:

The daily profit, P, of an oil refinery is given by

P = 8x − 0.02x2,

where x is the number of barrels of oil refined. How many barrels will give maximum profit and what is the maximum profit?


Answer


[Here's another way to find the maximum or minimum value of a parabola.]

Example 2:

A rectangular storage area is to be constructed along the side of a tall building. A security fence is required along the remaining 3 sides of the area. What is the maximum area that can be enclosed with 800 m of fencing?



Answer


Let's see how you do this sort of problem in LiveMath.

LIVEMath

 

Example 3

[This problem was presented for discussion earlier in the Differentiation introduction.]

A box with a square base has no top. If 64 cm2 of material is used, what is the maximum possible volume for the box?


Answer




Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

Recommended Math DVDs

get MathTutorDVDs

Easy to understand math lessons on DVD.
Broad range of math topics. Try before you commit.
MathTutorDVD.com


Book mark this page in Del.icio.us, Furl, Digg, StumbleUpon, whatever...


Didn't find what you are looking for? Try search:


Need a break? Play a math game. Well, they all involve math... No, really!

dumbolf memoTST bola shadow factory mindfields trick-hoops-challenge crystal clear