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x + 3y <= 12 multiply on 3 on both sides of equation to get

3x +9y <= 36. Then subtract the other equation from this to get 7y<=14 so y<=2.

Since you want the maximum number for P, choose y to be 2 and x ends up being 6. Therefore, largest value for P is 84 since 10(6) + 12(2).

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