aozgaa / x-y

maximize x^y subject to x,y>0 and x+y=8

Finds x and y non-negative doubles with x+y=8 that maximize x^y.

Solved in two ways:

1. numerical grid search
2. analytically

See blackpenredpen for a derivation of the analytic solution.

Build

(Only checked on Windows with Visual Studio 17 2022 build tools)

cmake -S . -B build -DCMAKE_EXPORT_COMPILE_COMMANDS=ON -G Ninja
cmake --build build

Run

.\build\xy.exe
3.5353999106882838532 :: 4.4646000893117161468 :: 280.90455671251208969
3.5354010355601515059 :: 4.4645989644398484941 :: 280.90455671267608295