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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