HK-PC 2019 Problem 6

If $57a + 88b + 125c \geq 1148$ , where $a,b,c > 0$ , what is the minimum value of $a^3 + b^3 + c^3 + 5a^2 + 5b^2 + 5c^2?$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.