Find the maximum value of P.F•dr, where F = 6xy?i + (3z - 10xy²)j+ (4y – 2x²y) k and C is a simple closed curve in the plane 5x + 3y + z= 8 oriented counterclockwise as seen from high on the z-axis. What curve C gives this maximum? The maximum value of which occurs when C is the boundary of the plane region 8 in 5x + 3y +z = 8 whose projection onto the xy-plane is (Type an exact answer.)

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