A project has four activities $$P,Q, R$$ and $$S$$ as shown below.

The normal cost of the project is Rs. $$10,000/-$$ and the overhead cost is Rs. $$200/-$$ per day. If the project duration has to be crashed down to $$9$$ days, the total cost (in Rupees) of the project is ______________.

If there are $$m$$ sources and $$n$$ destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is

A component can be produced by any of the four processes $${\rm I},$$ $${\rm II},$$ $${\rm III},$$ and $${\rm IV}$$. The fixed cost and the variable cost for each of the processes are listed below. The most economical process for producing a batch of $$100$$ pieces is

Consider the two states of stress as shown in configurations $${\rm I}$$ and $${\rm II}$$ in the figure below. From the standpoint of distortion energy (Von - Mises) criterion, which one of the following statements is true?