Question 3.2 (9 marks) Your friends have 40m of wire and wants to build the frame of a chicken coop as a rectangular cuboid shown here: They want to use all their wire and they also want that the volume of the block is as big as possible; it remains to determine the side lengths a, b, and c of the block that achieve this. Being in Week 9 of MAT9004, you are by now an expert in 2-variable optimisation so you've offered your friend to help them out by doing the following: a) Explain in detail how this problem is the same as nding the global maximum of a 2-variable func- tion; you can arrange that this function has variables a and I), call if f (a, 1)). Write down a formula for f(a, b) and determine a suitable domain D such that the answer to your problem is the global maximum of u, b) on D. b) Determine all stationary points of f (a, b) on D. 0) Determine the Hessian matrix of f(a, b) and classify each stationary point. d) Now do whatever is left to do in order to determine the global maximum of f (a, b) on D. e) What side lengths a, b, and c should your friend choose in order to get a block with maximal volume? What's the maximal volume