2007/08 AHSMC Part 1 Problem 6

Problem 6 of 16

The non-negative numbers $x$ and $y$ are such that $2x + y = 5$ . The sum of the maximum value of $x + y$ and the minimum value of $x + y$ is

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Solution

We have $2x+2y = 5+y \ge 5$ , so that the minimum value of $x+y$ is $\dfrac{5}{2}$ , attained at $(x, y) = \bigl(\dfrac{5}{2}, 0\bigr)$ . Also, $x + y = 5 - x \le 5$ , so that the maximum value of $x+y$ is $5$ , attained at $(x, y) = (0, 5)$ . The answer is (D).

University of Alberta

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