$($b$)$ Given the following information, construct the hypothetical phase diagram on Fig. $3$ for metals A and B

between room temperature $(20C)$ and $700C,$ given the following information and label the axes and the

phases present.

The melting temperature of metal $A$ is $550C.$

The maximum solubility of $B$ in $A$ is $8wt\%B,$ which occurs at $420C-$

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

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

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

The intermetallic compound $AB$ exists at a composition of $30wt\%B-70wt\%,$ and melts directly to

liquid at $525C.$

The melting temperature of metal $B$ is $600C.$

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

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