Problem $1(30$ points$)$ The parameter table given below shows a transportation problem formulation. Cost per Unit Distributed to Product $($Destination$)$ Source $1234($D$)$ Supply $141272404524029230753373021045$ 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?