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SMT 2023 Algebra #5

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May 3, 2023

Problem Statement

Suppose α,β,γ∈{−2,3}\alpha,\beta,\gamma\in\{-2,3\} are chosen such that M=max⁡x∈Rmin⁡y∈R≥0αx+βy+γxyM=\max_{x\in\mathbb{R}}\min_{y\in\mathbb{R}_{\ge0}}\alpha x+\beta y+\gamma xy is finite and positive (note: R≥0\mathbb{R}_{\ge0} is the set of nonnegative real numbers). What is the sum of the possible values of MM?
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