A department head has three tasks $($T$1,$ T$2,$ T$3)$ and four subordinates $($S$1,$ S$2,$ S$3,$ S$4)$ who can perform the tasks. The subordinates differ in efficiency, and the tasks differ in their intrinsic difficulty. His estimate of the times each person would take to perform each task is given in the effectiveness matrix below. How should the tasks be assigned $($no more than one task to each subordinate$),$ to minimize the total man$-$hours? Apply the Hungarian algorithm to solve the problem and find ALL the optimal assignments. Here we need to assign dummy row T$4?$