In this problem we identify a point (a, b) on the line 16x + 15y = 100 such that the sum of the distances from (−3, 0) to sa, bd and from (a, b) to (3, 0) is a minimum.

(a) Write a function f that gives the sum of the distances from (−3, 0) to a point (x, y) and from (x, y) to (3, 0). Let g(x, y) = 16x + 15y. Following the method of Lagrange multipliers, we wish to find the minimum value of f subject to the constraint g(x, y) = 100. Graph the constraint curve along with several level curves of f, and then use the graph to estimate the minimum value of f. What point (a, b) on the line minimizes f ?

(b) Verify that the gradient vectors ∇f(a, b) and ∇g(a, b) are parallel.