5. A rectangular box with a square base and no top is to be constructed from ve pieces of thin metal sheeting: one square piece with sides of length a: for the bottom of the box and four identical rectangular pieces of dimensions as x y for the four sides of the box. Each of the ve pieces is attached to the other pieces it touches by welding all along the edge where the pieces meet. The volume of the box must be maintained at 108 cm2. We want to minimize the total length of welded edges for the box. (a) (1 point) State the goal of the problem in just a few words. (b) (2 points) Write an equation for the quantity you are trying to minimize / maximize from part (a); this equation can contain multiple variables, but you must use the independent variable names given in the problem statement above to receive credit for this and the remaining problem parts. (0) (3 points) Use some other piece of information from the problem to write your equation from (b) in terms of only one independent variable. (d) (1 point) What is the domain of the independent variable in your equation in part (c)? Justify your answer. (e) (5 points) Now, find the value of your independent variable that optimizes your equation from part (c) on the domain from part (d). Be sure to justify your answer being a global extrema of the correct type