Question

A department head has four tasks to be performed and there are only three subordinates. The estimation of the time (in hours) each subordinate would take to perform is given below in table.
$$\begin{array}{cccc}\text{Tasks/Men}& A& B& C\\ P& 9& 24& 14\\ Q& 17& 29& 8\\ R& 37& 22& 18\\ S& 14& 32& 22\end{array}$$The tasks are allocated to each man in such a way such that total time is minimized. What will be the minimum time?

• A. 34 hours
• B. 31 hours
• C. 35 hours
• D. 39 hours

Answer 1

The correct option is D 39 hours

It is an unbalanced problem. For solving the problem we add a dummy subordinate.

$\begin{array}{ccccc}\text{Tasks/Men}& A& B& C& D\text{(Dummy)}\\ P& 9& 24& 14& 0\\ Q& 17& 29& 8& 0\\ R& 37& 22& 18& 0\\ S& 14& 32& 22& 0\end{array}$

Subtracting the smallest element of each column from all the elements of that column.

The optimum assignment is,
$P\to A,Q\to C,R\to B$ and $S$ for a dummy man

$\text{Minimum time = 9 + 8 + 22 = 39 hours}$