3. A carpenter, plumber, and engineer are available to perform certain tasks. Ea
ID: 336121 • Letter: 3
Question
3. A carpenter, plumber, and engineer are available to perform certain tasks. Each person can perform only one task in the allotted time. There are four tasks available, three of which must be done. The inefficiency matrix (think of this as a cost) for person i assigned to task j is as follows: Soldering Framing Drafting Wiring Carpenter 4 4 4 4 Engineer a) Which person should be assigned to which job? (Hint: Create a dummy person.) Which job will go unfinished? b) Now, suppose that each person can perform up to two tasks, and that all tasks must be done. What should the workers do?Explanation / Answer
a) Carpenter will do drafting (4)
Plumber will work on Wiring (3)
and Engineer will work on soldering (2)
Total cost = 4+3+2=9
As enginner and carpenter cost is 2 for soldering one should alloted. Plumbers lowest cost is for soldering and wiring, as soldering to be assignd to either enggineer or plumber so plumber will work on wiring. If carpenter alloted engineer need to work on framing which is of 5cost but in enginner works on soldering then carpener will work on drafting which is of 4 cost.
b) As each person can work on 2 type work and all work should finish, with above work distribution, farming will be done by plumber with 4 cost.
total cost = 9+4=13
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