The initial basic feasible solution of the following transportion problem : is…

Solution: Compute the total cost using the given basic feasible solution shipments.

Assignments (non-zero shipments from the basic feasible solution):

• O1 → D1 = 5

• O2 → D3 = 8

• O3 → D2 = 7

• O4 → D1 = 2

• O4 → D2 = 2

• O4 → D3 = 10

Compute the cost contribution of each non-zero shipment (unit costs taken from the cost table):

• O1 → D1: 5 × 2 = 10

• O2 → D3: 8 × 1 = 8

• O3 → D2: 7 × 4 = 28

• O4 → D1: 2 × 4 = 8

• O4 → D2: 2 × 1 = 2

• O4 → D3: 10 × 2 = 20

Add these contributions: 10 + 8 + 28 + 8 + 2 + 20 = 76.

Therefore the minimum (total) transportation cost for the given basic feasible solution is 76.

Remark: A common source of incorrect totals is misreading the unit cost for a cell (for example the cost from origin 4 to destination 3) or assigning the shipment amounts to the wrong destination. Re-check the placements and the unit costs when your sum differs from 76.