A firm has $\\$100,000$to invest in three projects. Project$A$requires$\$50,000$ and yields NPV $\\$80,000$. Project$B$requires$\$40,000$ and yields NPV $\\$60,000$. Project$C$requires$\$30,000$ and yields NPV $\\$50,000$. If the firm can invest in at most one of each project (binary selection), which combination maximizes the total Net Present Value (NPV) without exceeding the budget?