Problems: (you can use MATLAB or Python to perform necessary matrix computations) 1 A cardboard box for packing quantities of small foam balls is to be manufactured. The top, bottom, and front faces must be of double weight (i.e., two pieces of cardboard). A problem posed is to find the dimensions of such a box that maximize the volume for a given amount of cardboard, equal to 72 sq. ft. Find the optimal solution analytically using Lagrange mulitpliers. Next find the optimal solution using gradient descent algorithm and verify your result using Matlab fmincon () or Python scipy. optimize().