16Hit1600
AlgebraVery hardMaximum of a sum over a triangular region

Algebra practice question

In the xy-plane, a region consists of all points (x, y) satisfying y ≤ −x + 6, y ≥ 2, and x ≥ 1. What is the greatest possible value of x + y for a point in the region?

Answer: 6

On the edge y = −x + 6, x + y = 6, and every other point in the region lies below that edge, so x + y ≤ 6.

Common wrong answers

If you answered 3
3 is the value at the corner (1, 2), the minimum.
If you answered 7
7 would need a point above the line y = −x + 6.
If you answered 8
8 is the sum of the constants, not a value of x + y in the region.

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