Consider the transportation problem having the following parameter table:

Cost per Unit Distributed

Destination $($Product$)$

$12345($D$)$ Supply

$130251620080$

Source $225$ M $2532070$

$334252618060$

Demand $4050703020$

$(1)$ Create a mathematic model for the transportation problem.

$(2)$ Use Northwest corner rule to obtain an initial basic feasible solution