\begin{tabular}{|c|c|c|c|c|c|c|} \hline Project & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Net Present Value (\$ millions) & $17 & $7 & $15 & $16 & $22 & $11 \\ \hline Expenditure Required (\$ millions) & $91 & $35 & $82 & $71 & $115 & $51 \\ \hline \end{tabular} There are conditions that limit the investment alternatives: - At least two of projects 1,3,5, and 6 must be undertaken. - If either project 3 or 5 is undertaken, they must both be undertaken. - Project 4 cannot be undertaken unless both projects 1 and 3 also are undertaken. The budget for this investment period is $220 million. objective function in millions of dollars.) Max s.t. constraint on projects 1,3,5, and 6 constraint on projects 3 and 5 constraint on projects 1 and 4 constraint on projects 3 and 4 budget constraint (b) Solve the model formulated in part (a). What is the optimal net present value (in millions of dollars)? $ million How much of the budget is unused (in millions of dollars)