There are four projects under consideration. Each can be accepted or rejected (there is not partial funding). $2.1 million is available for funding. The table displayed funding needed and scores representing the estimated NPV (in $100 millions)

a) Formulate a zero-one linear optimization model to decide what projects to accept within the available budget.

b) Solve the linear programming relaxation to this problem Provide solution vector and solution value, find a feasible integer solution to the problem (by simple rounding). Indicate the difference between the upper and lower bounds.

c) Find the optimal solution by performing branch-and-bound for this knapsack problem, justify that it is the global optimum.

Project	A	B	C	D
Value	3	3	1	2
Cost ($K)	600	800	600	600