Question 1 (b) A company is considering to invest in eight projects. The estimated cost of each project, the perceived priority points, the estimated number of new jobs each project would create are provided in the Table 1. Table 1 Project Cost ($) Priority Points New Jobs X1 X2 X3 X4 X5 X6 X7 X8 5000 4500 600 2000 6000 800 3200 2500 3176 2774 3513 2928 4607 862 3829 2708 5 1 2 1 3 1 7 2 1. Formulate objective function for this 0-1 integer model to maximise the total number of perceived priority points. Considering the above problem write down mathematical equations for each of following conditions/constraints. 2. A budget of $21000 is available for the projects. 3. The company wishes to fund at most three of the projects. 4. The company wants to create at least 8 new jobs from these projects. 5. Only one of the two projects, i.e., X3 and X5 should be funded at this time but not both. 6. The company believes that if it decides to invest in project X7 then it should also invest in project X8, and vice versa. [DO NOT SOLVE THE ABOVE MODEL YOU DEVELOPED IN QUESTION 1 (b). Provide only formulation]
Question 1
(b)
A company is considering to invest in eight projects. The estimated cost of each project, the perceived priority points, the estimated number of new jobs each project would create are provided in the Table 1.
Table 1
|
Project |
Cost ($) |
Priority Points |
New Jobs |
|
X1 X2 X3 X4 X5 X6 X7 X8 |
5000 4500 600 2000 6000 800 3200 2500 |
3176 2774 3513 2928 4607 862 3829 2708 |
5 1 2 1 3 1 7 2 |
1. Formulate objective function for this 0-1 integer model to maximise the total number of perceived priority points.
Considering the above problem write down mathematical equations for each of following conditions/constraints.
2. A budget of $21000 is available for the projects.
3. The company wishes to fund at most three of the projects.
4. The company wants to create at least 8 new jobs from these projects.
5. Only one of the two projects, i.e., X3 and X5 should be funded at this time but not both.
6. The company believes that if it decides to invest in project X7 then it should also invest in project X8, and vice versa.
[DO NOT SOLVE THE ABOVE MODEL YOU DEVELOPED IN QUESTION 1 (b). Provide only formulation]
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