Find an initial solution to the following transportation problem.

a$)$ Use the northwest$-$corner method.

b$)$ Use the lowest cost cell method.

c$)$ Use the Vogel$$s Approximation method.

d$)$ What is the total cost of each method?

From

To

Supply Depo $1$ Depo $2$ Depo $3$

Plant $1$ $$6$ $$18$ $$8100$

Plant $2$ $$17$ $$13$ $$1960$

Plant $3$ $$20$ $$10$ $$2440$

Demand $508070$

$2.$ Using the U$-$V method to optimize the initial basic feasible solution found in question $(1).$

Compute the total cost.