Question 1: A shoe company's cost to manufacture a pair of football shoes is $10. The company charges $66 per pair for orders of 50 or fewer pairs. Larger orders are encouraged by a discount of $0.20 per pair for orders larger than 50 pairs. Find the largest order the company should allow to maximize profit.
Question 2: A movers and packers company wishes to design a open-top-box with square base whose volume is exactly 108 cubic feet. Find the dimensions of the box requiring the least amount of materials.