Boredom im Mathland
Writing final exams is boring, so one has to amuse oneself somehow. The following was the best I could do: Brand son of Bain son of Bard, Lord of Dale, calls out to his allies for aid. He wants a force 150 strong that can fire 1000 arrows per minute, and hew 200 orc necks per minute. His allies, Thranduil, Elvenking of Mirkwood, and Dain Ironfoot, King Under the Mountain, discuss how they can meet his request. Each elvish archer can fire 8 arrows per minute, but those dainty elvish knives take 2 minutes to cut off a single orcish neck. A doughty dwarven warrior can barely shoot at all (1 arrow per minute), but they can decapitate 2 orcs per minute. What mix of dwarves and elves comes closest (in the least squares sense) to meeting Brand's needs?