Q$\mathrm{.}2($a$)$ The data for the transportation problem is given in the following table. The total supply is

$20$ units, and the total demand is $24$ units. Determine a minimum$-$cost shipping schedule

that distributes the entire $20$ units among five destinations.

$($b$)$ Consider a transportation problem having $m$ supply sources, $n$ demand centers, $c_{ij}$ being

the unit cost of transportation, $x_{ij}$ being the number of units transported from the $i-$th

supply source to the $j-$th demand center. Write the linear programming formulation of the

transportation problem and its dual. Derive the optimality criterion of the MODI method

using complementary slackness conditions.Q$\mathrm{.}2($a$)$ The data for the transportation problem is given in the following table. The total supply is

$20$ units, and the total demand is $24$ units. Determine a minimum$-$cost shipping schedule

that distributes the entire $20$ units among five destinations.