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Example: Unconstrained Optimization

Let's start with an example. Suppose the function P(x,y) = 3xy - x³ - y³ represents the profit (in millions) for selling x thousands of product A and y thousands of product B. We want to find out how many of each product to sell in order to maximize our profit.

What Happens at Maxima and Minima?
Finding the Critical Points
Testing the Critical Points Graphically
Testing the Critical Points Analytically
Putting it All Together

Vector Calculus
12/6/1997