Exercise 2- Optimising volumes. (10pts total) Find the maximum volume of a 3D box, whose edges are perfectly parallel to the coordinate axes, that fits inside the ellipsoid defined by 4x2y24z2=3, as shown in the Figure below. To answer this question, proceed as follows.(1) Give an objective function f(x,y,z) which can be used to describe volumes of boxes with edges parallel to the coordinate axes. Do not forget to specify f's domain.(2) Give a function g(x,y,z) which can be used to describe the constraining ellipsoid;(3) Re-formulate the question as a constrained optimisation problem, and solve it using the method of Lagrange multipliers. Do not forget to take into account eventual boundaries (whether you need to consider boundaries depends on how you specified f's domain).Without loss of generality, you may assume that the box's corners lie on the ellipsoid.