The path $C$ is a line segment of length 15 in the plane starting at $(1,4)$. For $f(x,y) = 4 x + 3 y$, consider $$\int_C \nabla f \cdot d\vec r.$$

(a) Where should the other end of the line segment $C$ be placed to maximize the value of the integral?
At $x =$ , $y =$

(b) What is the maximum value of the integral?
maximum value =