Section 3.7, Optimization Problems
A Scenario
Let’s pretend I have an Etsy shop and I want to sell an open-topped, square-based box with a volume of 32,000 cubic centimeters. 1.
What dimensions should I make the box (length, width, height) in order to minimize the amount of material used?
Example
If $x$ and $y$ are positive numbers so that $x+y = 32$, find values of $x$ and $y$ that maximize $P=x^{10}y^2$
Example
You are sitting in a row boat (in perfectly still water), 5 miles from a perfectly straight shoreline. You want to be at point B. If you can row 2mph and walk 4mph, at what point to the right of A should you land your boat in order to minimize the amount of time traveled?
That’s a little more than 8 gallons for us Imperialists. I don’t know what hipster thing we’ll keep in it. Maybe fish. ↩︎