$($b$)$ Given the following information, construct the hypothetical phase diagram on Fig. $3$ for metals A and B between room temperature $(20\backslash$deg C$)$ and $700\backslash$deg C$,$ given the following information and label the axes and the phases present.

The melting temperature of metal A is $550\backslash$deg C$.$

The maximum solubility of B in A is $8$ wt$\%$ B$,$ which occurs at $420\backslash$deg C$.$ r

The solubility of B in A at room temperature is $0$ wt$\%$ B$.$

One eutectic occurs at $420\backslash$deg C and $18$ wt$\%$ B$-82$ wt$\%$ A$.$

A second eutectic occurs at $475\backslash$deg C and $60$ wt$\%$ B$-40$ wt$\%$ A$.$

The intermetallic compound AB exists at a composition of $30$ wt$\%$ B$-70$ wt$\%$ A$,$ and melts directly to liquid at $525\backslash$deg C$.$

The melting temperature of metal B is $600\backslash$deg C$.$

The maximum solubility of A in B is $13$ wt$\%$ A$,$ which occurs at $475\backslash$deg C$.$

The solubility of A in B at room temperature is $3$ wt$\%$ A$.$