Differential Calculus 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... show more 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 fi nd 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.
2 answers 2