
Explanation of Solution
Selecting the project using the preemptive goal
Consider the following variables
For every project values related to each attribute are tabulated.
The table is given below,
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
ROI | 2070 | 456 | 670 | 350 | 495 | 380 | 1500 | 480 |
Cost | 900 | 240 | 335 | 700 | 410 | 190 | 500 | 160 |
Productivity improvement | 3 | 2 | 2 | 0 | 1 | 0 | 3 | 2 |
Manpower needed | 18 | 18 | 27 | 36 | 42 | 6 | 48 | 24 |
Degree of risk | 3 | 2 | 4 | 1 | 1 | 0 | 2 | 3 |
The company has the following goals.
Goal 1: Archive a return on investment of at least
Goal 2: Limit cost to
Goal 3: Archive a productivity improvement of at least 6. Thus the constraint formed is,
Goal 4: Limit manpower use to 108. Thus the constraint formed is,
Goal 5: Limit technological risk to a total of 4. Thus the constraint formed is
Hence the linear programming can be formulated as given below,
Minimize
Subject to the constraints,
Here, it is observed that for these set of constraints, there is no region which is feasible. That is all the constraints cannot be met. Hence e assign a cost value incurred if any of the goal is not meet. So introduce deviational variables as follows

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Chapter 4 Solutions
Introduction to mathematical programming
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