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?
[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?
Let's see how you do this sort of problem in 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?
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