Chemco is considering four projects to invest on. Chemco will earn a net present value (NPV) of $16,000 from Project 1; an NPV of $22,000 from Project 2; an NPV of $12,000 from Project 3; and an NPV of $8,000 from Project 4. Each Project requires a certain cash outflow at the present time: Project 1, $6,000; Project 2,$8,000; Project 3, $3,000; and Project 4, $4,000. Currently, $14,000 is available for all the investment. Aim of the Chemco is to maximize their NPV by investing on the projects they choose. Project 1 Project 2 Project 3 Project 4 NPV $16,000 $22,000 $12,000 $8,000 Investment $6,000 $8,000 $3,000 $4,000 a. (10 pts) With total enumaration, find all possible solutions for the problem given. Find total investment and total NPV (objective function value) of each of the solution. b. (10 pts) Mention the type of the solutions you found in part a as feasible, infeasible or optimal. C. (15 pts) Find a heuristic approach different than the bang-for-buck approach we discussed in the class to solve this problem. Is your solution optimal? If not find the absolute and relative gap of this solution with the optimal solution. d. (15 pts) Formulate a mathematical model to maximize total NPV. Clearly define your decision variables, objective function and constraints. e. (10 pts) Assume that Chemco has to finish the projects which they invest on in 24 months. Each project has a duration as given below; Project 1 Project 2 Project 3 Project 4 Duration (months) 12 13 8 5 Projects cannot be done simultaneously. In other words, to start a new project, the previous one must be finished. Which feasible solutions in part bare infeasible now? What is the optimal solution now? Chemco is considering four projects to invest on. Chemco will earn a net present value (NPV) of $16,000 from Project 1; an NPV of $22,000 from Project 2; an NPV of $12,000 from Project 3; and an NPV of $8,000 from Project 4. Each Project requires a certain cash outflow at the present time: Project 1, $6,000; Project 2,$8,000; Project 3, $3,000; and Project 4, $4,000. Currently, $14,000 is available for all the investment. Aim of the Chemco is to maximize their NPV by investing on the projects they choose. Project 1 Project 2 Project 3 Project 4 NPV $16,000 $22,000 $12,000 $8,000 Investment $6,000 $8,000 $3,000 $4,000 a. (10 pts) With total enumaration, find all possible solutions for the problem given. Find total investment and total NPV (objective function value) of each of the solution. b. (10 pts) Mention the type of the solutions you found in part a as feasible, infeasible or optimal. C. (15 pts) Find a heuristic approach different than the bang-for-buck approach we discussed in the class to solve this problem. Is your solution optimal? If not find the absolute and relative gap of this solution with the optimal solution. d. (15 pts) Formulate a mathematical model to maximize total NPV. Clearly define your decision variables, objective function and constraints. e. (10 pts) Assume that Chemco has to finish the projects which they invest on in 24 months. Each project has a duration as given below; Project 1 Project 2 Project 3 Project 4 Duration (months) 12 13 8 5 Projects cannot be done simultaneously. In other words, to start a new project, the previous one must be finished. Which feasible solutions in part bare infeasible now? What is the optimal solution now
