MathDB

2015 E8

Part of MBMT Team Rounds

Problems(1)

MBMT Team -- Euler #8

Source:

3/29/2015
You are trying to maximize a function of the form f(x,y,z)=ax+by+czf(x, y, z) = ax + by + cz, where aa, bb, and cc are constants. You know that f(3,1,1)>f(2,1,1)f(3, 1, 1) > f(2, 1, 1), f(2,2,3)>f(2,3,4)f(2, 2, 3) > f(2, 3, 4), and f(3,3,4)>f(3,3,3)f(3, 3, 4) > f(3, 3, 3). For −5≤x,y,z≤5-5 \le x,y,z \le 5, what value of (x,y,z)(x,y,z) maximizes the value of f(x,y,z)f(x, y, z)? Give your answer as an ordered triple.