To solve the problem of assigning programmers to application programs in such a way that the total computer time is minimized, we can use the Hungarian method or systematic enumeration. Below, I'll demonstrate how to frame this problem and suggest a possible solution without going through the full mathematical calculations or algorithmic steps.
Problem Representation:
We have three programmers (P1, P2, P3) and three programs (A, B, C) with the estimated computer time (in minutes) to complete the programs:
| | Program A | Program B | Program C | |--------|-----------|-----------|-----------| | P1 | 120 | 100 | 80 | | P2 | 80 | 90 | 110 | | P3 | 110 | 140 | 120 |
Objective:
Minimize the total time taken to complete all programs by assigning each programmer to one unique program.
Total time calculation:
To minimize the total time, we would ideally want to look for combinations of programmer-to-program assignments that yield the lowest cumulative estimated time.
Finding the Optimal Assignment:
We can evaluate the different combinations and their total times, or apply an algorithm for optimization.
- All possible assignments:
- P1 to A, P2 to B, P3 to C: 120 + 90 + 120 = 330
- P1 to A, P2 to C, P3 to B: 120 + 110 + 140 = 370
- P1 to B, P2 to A, P3 to C: 100 + 80 + 120 = 300
- P1 to B, P2 to C, P3 to A: 100 + 110 + 110 = 320
- P1 to C, P2 to A, P3 to B: 80 + 80 + 140 = 300
- P1 to C, P2 to B, P3 to A: 80 + 90 + 110 = 280
After evaluating all possible assignments, we notice:
- P1 to C, P2 to A, P3 to B yields the least total time of 280 minutes.
Conclusion:
To minimize the total computer time:
- Assign Programmer 1 to Program C.
- Assign Programmer 2 to Program A.
- Assign Programmer 3 to Program B.
This configuration provides the minimum total time of 280 minutes for all three programmers to complete the assigned programs.