The total number of decision variables in the objective function of an assignment problem of size $$n\,\, \times \,\,n$$ ($$n$$ jobs and $$n$$ machines) is

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be ________ minutes (in integer).

A firm is required to procure three items $$(P, Q$$ and $$R).$$ The prices quoted for these items (in Rs.) by suppliers $${S_1},{S_2},$$ and $${S_3}$$ are given in table. The management policy requires that each item has to be supplied by only one supplier and one supplier supply only one item. The minimum total cost (in Rs.) of procurement to the firm is: