Given below is a basic feasible solution to a transportation problem with three supply points $$(A,B,C)$$ and three demand points $$(P, Q, R)$$ that minimizes cost of transportation in the standard tabular format.

$$(a)$$$$\,\,\,\,\,\,\,\,$$ Compute the cost corresponding to the present solution
$$(b)$$$$\,\,\,\,\,\,\,\,$$ It is optimal?
$$(c)$$$$\,\,\,\,\,\,\,\,$$ Does an alternate optimum exist ?

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 $$D.$$