In a concentric counter flow heat exchanger, water flows through the inner tube at $${25^ \circ }C$$ and leaves at $${42^ \circ }C$$. The engine oil enters at $${100^ \circ }C$$ and flows in the annular flow passage. The exit temperature of the engine oil is $${50^ \circ }C.$$ Mass flow rate of water and the engine oil are $$1.5kg/s$$ and $$1$$ $$kg/s,$$ respectively. The specific heat of water and oil are $$4178$$ $$J/kg.K$$ and $$2130$$ $$J/kg.K,$$ respectively. The effectiveness of this heat exchanger is _________.

Consider the following data with reference to elementary deterministic economic order quantity model

The total number of economic orders per year to meet the annual demand is _______________.

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