A pyramid with known bottom edge length a and height h is to be inscribed with a cuboid with square base area (side length x and height y), which has maximum volume.
(a) Formulate the nonlinear optimization problem with constraints.
(b) Give the optimal solution.

(05.02) mr. morris is going to save money and replace his sailboat's mainsail himself. he must determine the area of the mainsail in order to buy the correct amount of material. calculate the area of the parallelogram to determine how much material should be purchased. be sure to explain how to decompose this shape into rectangles and triangles. describe their dimensions and show your work.