Analytics Modelling for my personal blog

You wish to invest S$50,000. You have identified five investment opportunities. Each is an
“all-or-nothing” investment: you must invest the full amount or not invest at all.

• Investment1 requires an investment of S$16,000 and has a present value (a time-discounted
value) of S$23,000;
• Investment 2 requires S$14,000 and has a present value of S$25,000;
• Investment 3 requires S$22,000 and has a present value of S$28,000;
• Investment 4 requires S$12,000 and has a present value of S$14,000; and
• Investment 5 requires S$38,000 and has a present value of S$49,000.

Into which investments should you place your money so as to maximise your total present value?

Solve this problem using Branch and Bound, showing the full tree you develop (omitting pruned branches), and clearly explaining why certain subproblems are fathomed. For each intermediate subproblem, solve the Linear Programming associated to that problem using Xpress Mosel. Include in your submission the Xpress formulation and Xpress output for each sub-problem investigated.