$9\mathrm{.}3-6.$ Reconsider Prob. $9\mathrm{.}1-6.$ Now assume that distribution centers $1,2,$ and $3$ must receive exactly $10,20,$ and $30$ units per week, respectively. For administrative convenience, management has decided that each distribution center will be supplied totally by a single plant, so that one plant will supply one distribution center and the other plant will supply the other two distribution centers. The choice of these assignments of plants to distribution centers is to be made solely on the basis of minimizing total shipping cost.

$($a$)$ Formulate this problem as an assignment problem by constructing the appropriate cost table, including identifying the corresponding assignees and tasks.

c $($b$)$ Obtain an optimal solution.

$($c$)$ Reformulate this assignment problem as an equivalent transportation problem $($with four sources$)$ by constructing the appropriate parameter table.

$9\mathrm{.}1-6.$ The Move$-$It Company has two plants producing forklift trucks that then are shipped to three distribution centers. The production costs are the same at the two plants, and the cost of shipping for each truck is shown for each combination of plant and distribution center:

$\backslash$table$[[,,$Distribution Center$],[,,1,2,3],[$Plant$,$A$,$$$800,$$$700,$$$400$