Construct the hypothetical phase diagram for metals A and $B$ between room temperature $(20C)$ and $700C,$ given the following information.

The melting temperature of metal $A$ is $480C.$

The maximum solubility of $B$ in $A$ is $4$ wt $\%$ B$,$ which occurs at $420C.$

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

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

A second eutectic occurs at $475C$ and $42wt\%B-58wt\%A.$

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

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

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

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