Four different machines can do any of the three required jobs, with different profits resulting from each assignment as shown below:JobsMachine A (₹)Machine B (₹)Machine C (₹)Machine D (₹)135404341240484443350454648Find the optimal assignment schedul…

Answer: Job 1 → C, Job 2 → B, Job 3 → A (machine D idle); maximum profit ₹ 141

The matrix is not square, so add a dummy job 4 with zero profits. To convert the maximization problem to minimization, subtract every entry from the largest entry 50 (loss matrix):

Row minimum subtraction (7, 2, 0, 50); column minima are then all 0:

Zeros can be assigned one in each row and column: Job 1 → C, Job 2 → B, Job 3 → A, Dummy → D. The minimum number of lines covering all zeros is 4 = order of matrix, so this assignment is optimal.

Maximum profit \(=43+48+50=\)₹ 141. Machine D is not assigned any job.