Consider station k of the assembly line scheduling problem. The variable f$1[$k$]$ is the fastest way to get through station k on line $1,$ and f$2[$k$]$ is the fastest way to get through station k on line $2.$ Assume f$1[$k$]$ was achieved by doing a transfer from line $2$ and paying t$2.$ Is it possible that f$2[$k$]$ was achieved by transferring from line $1$ and paying t$1?$ Assume all transfer fees are positive numbers. You must prove mathematically.