(Solved): the runner needs to go from point A to the river which is the blue line and go back to A from the r ...

the runner needs to go from point A to the river which is the blue line and go back to A from the river.

Y A B X (1) Rephrase the first variant of the runner's problem as a constrained optimization problem (given that (2, 2), and assuming that the river is given by the equation g(x, y) = 0). the starting point is A = a. What is the function f(x, y) being optimized? b. Describe and sketch the level curves of the function f(x, y). c. Suppose that the runner starts at point A = (2, 2), and the river is given as in the picture above. Find the point P on the river that minimizes the total length of the runner's path. (Hint: It is easier to do this geometrically, rather than algebraically.)