QUESTION $2(60$ points$)$

A factory which produces towels, has $4$ warehouses and $2$ stores. There are $10,9,7$ and $8$ boxes of

towels in the warehouses respectively. The company has committed to send $5$ units of towels to

Store $1$ and $8$ units to Store $2$ from its warehouses. Additionally, at the end of the month, there

should be $6$ units of towels in warehouse $2,10$ units in warehouse $3$ and $4$ units in warehouse $4.$

The transportation costs of these products are given in the below figure.

Napal

a$.$ Balance the temporary accommodation problem using the transportation table to minimize

transportation costs.

b$.$ Find a basic feasible solution for the problem you have formulated using the Northwest

Corner Method.

c$.$ Find a basic feasible solution for the problem you have formulated using the Least Cost

Method.

d$.$ Find a basic feasible solution for the problem you have formulated using the Vogel

Approximation Method.

e$.$ Solve the problem with the Transportation Simplex, starting from the basic feasible solution

you found with the Vogel Approximation Method in question d$.$