Three Absolute Values on a Diamond

★ 7/10Linear Programming Absolute Value algebra analytic geometry inequality

Problem

Find the least real $a$ such that

\left|2x - 3y + \frac32\right| + |y - 1| + |2y - x - 3| \le a

holds for all $x, y$ with $|x| + |y| \le 1$ .

Answer

Solution

Difficulty	7/10
Topics	Linear Programming, Absolute Value, algebra, analytic geometry, inequality

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