The corner points for a closed and bounded feasible solution

The corner points for a closed and bounded feasible solution region are (20, 0), (0, 0), (0, 25), (5, 15), (15, 10). If the original objective was to maximize the function P = 8x + 6y, which corner point(s) yield the optimal solution?

Solution

P = 8x+6y

P(20,0) = 160

P(0,0) =0

P(0,25) = 150

P(5,15) = 40 + 90 = 130

P(15,10) = 120 + 60 = 180

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So

Maximum value is 120

so (15,10) is a optimal solution