Optimization Questions

An objective function $Z=ax+by$ is maximum at points $(9,3)$ and $(5,7)$. If $a,b\ge 0$ and $ab=16$, then the maximum value of the function is:

Ashok bought tables and chairs for a marriage hall. The cost of a table is $₹2500$ and a chair is $₹500$. He has a budget of $₹60000$ and space for at most $60$ items. If the profit is $₹75$ per table and $₹25$ per chair, find the maximum profit.