A wire is being cold drawn and the average value of flow stress in the process $(Y_f)$ is equal to the yield strength of the wire after it has been cold worked. It is known that the drawing force required during wire drawing is given by the formula ${?}_{\text{F}\text{o}\text{r}\text{c}\text{e}}={}_{,}{A}_{2}lo{g}_{}(\frac{A_1}{A_2})$ where $A_1$ is the initial area of the wire being drawn and $A_2$ is the final area of the wire after drawing. Calculate the highest ratio between the diameter of initial and final diameter of the wire.

$(5)$