1. A closed rectangular box with a volume of 15 ft"3 is made from two kinds of materials. The top and bottom are made of material costing 10 per square foot and the sides from material costing 5 per square foot. Find the dimensions of the box so that the cost of materials is minimized. 2. Consider the function flay] =43\" 3y2 + 2M over the unit square 0 s x s 1, D s v s 1. {a} Find the maximum and minimum values of f on each edge of the square. lb} Find the maximum and minimum values of f on each diagonal of the square. {c} Find the maximum and minimum values of {on the entire square