A Non-Unique Optimum

★ 6/10Linear Programming algebra analytic geometry inequality vectors

Problem

Real numbers $x, y$ satisfy the constraints

\begin{cases} x + y - 2 \leqslant 0,\\ x - 2y - 2 \leqslant 0,\\ 2x - y + 2 \geqslant 0. \end{cases}

If the objective $z = y - ax$ attains its maximum at more than one point of the feasible region, find all possible values of the real number $a$ .

Answer

Solution

Difficulty	6/10
Topics	Linear Programming, algebra, analytic geometry, inequality, vectors

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