1

Part of 2003 Swedish Mathematical Competition

Problems(1)

min x if y = x - 2003, z = 2y - 2003, w = 3z - 2003 ofr x,y,z,ww>=0

Source: 2003 Swedish Mathematical Competition p1

x, y, z, w

are nonnegative real numbers satisfying

\left\{ \begin{array}{l}y = x - 2003 \\ z = 2y - 2003 \\ w = 3z - 2003 \\ \end{array} \right.

find the smallest possible value of

x

and the values of

y, z, w

corresponding to it.

algebraminsystem of equationsSysteminequalities