1. Find the isosceles triangle of smallest area (Figure) that circumscribes a circle of radius 1 (from Thomas Simpson's The Doctrine and Application of Fluxions, a calculus text that appeared in 1750).
2. A box of volume 72 m3 with a square bottom and no top is constructed out of two different materials. The cost of the bottom is $40/m2 and the cost of the sides is $30/m2. Find the dimensions of the box that minimize total cost.