Fig. P$8\mathrm{.}1$ and P$8.2$

$8\mathrm{.}2$ Two solid cylindrical rods $AB$ and $BC$ are welded together at $B$ and loaded as shown. Knowing that the average normal stress must not exceed $175$ MPa in rod $AB$ and $150$ MPa in rod $BC,$ determine the smallest allowable values of $d_1$ and $d_2.$