$9\mathrm{.}3-6.$ 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 con$-$structing the appropriate cost table, including identifying the corresponding assignees and tasks.

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

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