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To test the convexity of the given set: \[ S = \{(x,y) \mid x + y \leq 8 \text{ or } 2x + y \leq 10, x \geq 0, y \geq 0\} \] ### Step 1: Understanding the Set - The constraints define two half-spaces: 1. \( x + y \leq 8 \) (a region below the line \( x + y = 8 \)) 2. \( 2x + y \leq 10 \) (a region below _____ ___ __________ ______ ____.
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