$A$ block of mass $m_{2}$ is placed on a horizontal table and another block of mass $m_{1}$ is placed on top of it. An increasing horizontal force $F=\alpha t$ is exerted on the upper block, but the lower block never moves as a result. If the coefficient of friction between the blocks is $\mu_{1}$ and that between the lower block and the table is $\mu_{2}$, then what is the maximum possible value of $\mu_{1} / \mu_{2}$?

• A
  $\frac{m_{2}}{m_{1}}$
• B
  $1+\frac{m_{2}}{m_{1}}$
• C
  $\frac{m_{1}}{m_{2}}$
• D
  $1+\frac{m_{1}}{m_{2}}$