\(\mbox{We want to maximize }x y \mbox{ subject to }x+y=22\\ y=22-x \\ x y = (22-x)x = 22x - x^2 = -(x^2-22x) = \\ -((x-11)^2-121) = 121-(x-11)^2 \\ \mbox{This has a maximum value of }121 \mbox{ at }x=y=11\)
\(\mbox{We want to maximize }x y \mbox{ subject to }x+y=22\\ y=22-x \\ x y = (22-x)x = 22x - x^2 = -(x^2-22x) = \\ -((x-11)^2-121) = 121-(x-11)^2 \\ \mbox{This has a maximum value of }121 \mbox{ at }x=y=11\)
Well, I don't know what to make of your puzzle!!!!. To me: 21! X 1!=5.1 X 10^19, if that's acceptable to you? I know that 22/2=11 X 11=121, but that's peanuts compared to the number before it!!!.
