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# Calculus (differential) Optimization Problem?

Suppose x; y, and z are positive numbers that sum to 10. What is the largest possible value of xy + xz + yz?

(a) First, suppose that z is a fixed parameter. Then we have to find nonnegative numbers x and y (depending on the fixed value z such that x+y = 10-z), such that xy + xz + yz is maximized.

(b) To find the global maximum, plug in the values for x and y obtained in (a) in

order to rewrite xy + xz + yz as a function of a single variable. Then maximize

this function.

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