Because the objective is to maximize, convert the profit matrix into a loss matrix using $24-a_{ij}$ (subtract from the largest entry), then apply row reduction, column reduction and the Hungarian method. A complete set of five independent zeros gives the optimal assignment $1\to\text{II},\,2\to\text{V},\,3\to\text{I},\,4\to\text{III},\,5\to\text{IV}$ with maximum profit $111$.

Given profit matrix (rows $=$ jobs $1$–$5$, columns $=$ machines I–V):

Step 1 — Convert to a minimization problem. The largest entry is $24$. Replace each element by $24-a_{ij}$ to get the opportunity-loss matrix:

Step 2 — Row reduction. Subtract the smallest entry of each row (row minima $0,2,1,3,1$):

Step 3 — Column reduction. Subtract the smallest entry of each column (column minima $1,0,0,1,0$):

Step 4 — Make the assignment (Hungarian method). Assign one zero per row and column:

• Row 1 has a single zero at II $\Rightarrow 1\to\text{II}$. …