#8) (50 points) In a project organization, there are 3 ongoing projects with one year left for their completion. Five project proposals are proposed to the organization each with a 3-year time horizon. The financial resources available to the organization for the next 3 years are estimated as B1, B2, B3. The expenditure of each project i for these resources in year t are estimated as Cit, i=1,2,3,4,5 and +1,2,3. The expenditures for the ongoing projects are estimated to be Ck, k = 1,2,3. Further resources needed are lab bench space (S) and human resources (H), which are expected to stay constant over the time horizon. The demand of each project i for these resources in year t are estimated as Sit and hit. The demands for the ongoing projects are estimated to be 5k and hk. The benefit to be obtained from each project proposed is calculated as a. The benefits will be accrued at the end of the time horizon once the project is completed. Write a mathematical programming formulation so as to maximize the NPV of the benefits obtained from the portfolio selected at an interest rate of 10% per year. #9) (50 points) In the Multi-Objective Mathematical Programming Model for Project Selection and Scheduling, make the necessary changes in the constraint sets to accomodate the case where the amount not spent of the finances available at the beginning of the period is transferrred to the next period. (Hint: Make use of the analogy with the production-inventory models.) #8) (50 points) In a project organization, there are 3 ongoing projects with one year left for their completion. Five project proposals are proposed to the organization each with a 3-year time horizon. The financial resources available to the organization for the next 3 years are estimated as B1, B2, B3. The expenditure of each project i for these resources in year t are estimated as Cit, i=1,2,3,4,5 and +1,2,3. The expenditures for the ongoing projects are estimated to be Ck, k = 1,2,3. Further resources needed are lab bench space (S) and human resources (H), which are expected to stay constant over the time horizon. The demand of each project i for these resources in year t are estimated as Sit and hit. The demands for the ongoing projects are estimated to be 5k and hk. The benefit to be obtained from each project proposed is calculated as a. The benefits will be accrued at the end of the time horizon once the project is completed. Write a mathematical programming formulation so as to maximize the NPV of the benefits obtained from the portfolio selected at an interest rate of 10% per year. #9) (50 points) In the Multi-Objective Mathematical Programming Model for Project Selection and Scheduling, make the necessary changes in the constraint sets to accomodate the case where the amount not spent of the finances available at the beginning of the period is transferrred to the next period. (Hint: Make use of the analogy with the production-inventory models.)