The parameter table given below shows a transportation problem formulation.

Cost per Unit Distributed to Product $($Destination$)$

Source $1234($D$)$ Supply

$1412724045$

$2402923075$

$3373021045$

Demand $20304075$

$($a$)$ Find a basic feasible solution using the Northwest Corner method.

$($b$)$ Use Vogel's approximation method to find another basic feasible solution and compare

its objective value to the one found by the Northwest Corner method $($better or worse?$).$

Do not solve to optimality.

$($c$)$ The transportation simplex has been applied and at some iteration the basic variables

have the following values:

x$12=30$ x$14=15$ x$21=15$ x$24=60$ x$31=5$ x$33=40$

Perform a complete transportation simplex iteration $($identify the entering variable,

leaving variable, and find the new basic feasible solution$).$ Is the new solution optimal?