Solve the linear programming problem by sketching the region and labeling the vertices, deciding whether a solution exists, and then finding it if it does exist. (If an answer does not exist, enter DNE.)
Maximize P = 10x + 6y
Subject to
2x + y ≤ 90
x + y ≤ 50
x + 2y ≤ 90
x ≥ 0, y ≥ 0
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