A company rents three warehouses $$A, B$$ and $$C$$ from which they supply bearings to two customers $$P$$ and $$Q.$$ The profit per piece, the annual demands of the customers and the supplies available from the warehouses are shown below:

As the company is not able to meet the demands, it is proposed to replace warehouse $$C$$ with a warehouse rented at $$D$$ whose supply capacity would be $$5000.$$ The expected profit would be Rs.$$6$$ and Rs.$$5$$ per piece distributed to $$P$$ and $$Q$$ respectively. The rental charges for warehouse $$D$$ is Rs.$$5,000$$ per year. Find the increase in the profit of the company after replacing warehouse $$C$$ by $$D.$$

A small element at the critical section of a component in bi-axial state of stress with the two principal stresses being $$360$$ $$MPa$$ and $$140$$ $$MPa.$$ The maximum working stress according to distortion energy theory is

To make a worm drive reversible, it is necessary to increase

The dynamic load capacity of $$6306$$ bearing is $$22KN.$$ The maximum radial load it can sustain to operate at $$600$$ $$rev/min,$$ for $$2000$$ hours is