Question

Example: o1.A computer center has three programmers. The center wants three application programs to be developed. The head of the computer center, after studying carefully the programs to be developed, estimate the computer time in minutes required by the experts for the application programs as follows: D Assign the programmers to the programs in such a way that the total computer time is minimum. Programnmers 2 3 Cont.. Programs (estimated time in A minutes) 120 80 Cont... 110 B 100 90 140 C 80 110 120

Answer 1

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.

1. **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.