Queen Chloe is planning to build a castle inside of arectangular moat. A river runs horizontally along the bottom of herland, and that river will form the bottom of the moat, but theother three sides must be dug by a ditch digging company. For thetwo vertical sections of the moat, the company will charge 1 goldpiece per meter. But because the moat digging becomes easierfurther from the river, the company offers a discount to digfurther from the river on the horizontal section. For thehorizontal section, the price per meter is 1 gold piece divided bythe vertical distance from the river.
If Queen Chloe has 12 gold pieces, what are the dimensions ofthe moat that will give her the maximum area for her castle? How doyou know that these dimensions maximize the area?
