a. A farmer has 1800 m of fencing to make two equal rectangular pens that share  a common side. Determine the dimensions of each pen so that the area is a maximum.

b. The perimeter of an isosceles triangle is 38 m. Find the length of the sides of the  triangle of maximum area.

c. An open-topped storage box with a square base has a capacity of 5 m3. The  material for the sides cost $1.60/m2, while the material for the bottom costs $2.00/ m2. Find the dimensions that will minimize the cost of making the box.

d. A cardboard box manufacturer wishes to make open boxes from pieces of  cardboard 12 cm square by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the square to be cut out in order to obtain a box of the largest possible volume.