Let a, b, c, d, e, f be positive real numbers such that a + b + c + d + e + f = 7. Find the minimum value of 1/a + 4/b + 9/c + 16/d + 25/e + 36/f.
The minimum vaue occurs when a = b = c = d = e = f = 7/6. Then 1/a + 4/b + 9/c + 16/d + 25/e + 36/f = 78.
