Find the maximum and minimum values of f subject to the given constraints. use a computer algebra system to solve the system of equations that arises in using lagrange multipliers. (if your cas finds only one solution, you may need to use additional commands. round your answer to four decimal places.) f(x, y, z) = yex − z; 9x2 + 4y2 + 36z2 = 36, xy + yz = 1

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.