Objective of the transportation problem:
The transportation problem is a classic optimization problem in operations research. It involves allocating a set of goods from a set of sources to a set of destinations in the most efficient and cost-effective manner. The objective of the transportation problem is to determine the optimal transportation plan that minimizes the overall cost or maximizes the total profit.

Maximizing total profit:
In the context of the transportation problem, the objective of maximizing the total profit means that we aim to find the transportation plan that generates the highest possible profit. This is achieved by assigning goods from sources to destinations in such a way that maximizes the revenue and minimizes the cost associated with transportation.

Profit in the transportation problem:
The profit in the transportation problem is usually calculated as the difference between the revenue generated from selling the goods at the destination and the cost incurred in transporting the goods from the source to the destination. The revenue is determined by the selling price of the goods and the quantity delivered to each destination. The cost is determined by factors such as transportation distance, mode of transportation, and other associated costs.

Optimal cost:
While the transportation problem also involves minimizing the overall cost, it is not the objective to be maximized. The optimal cost refers to the minimum cost required to transport the goods from sources to destinations while satisfying the supply and demand constraints. Minimizing the cost is one of the constraints in the transportation problem, but it is not the objective to be maximized.

Conclusion:
In summary, the objective of the transportation problem is to maximize the total profit by finding the optimal transportation plan that maximizes the revenue and minimizes the cost. The transportation problem involves allocating goods from sources to destinations in an efficient and cost-effective manner. While minimizing the overall cost is an important constraint in the transportation problem, it is not the objective to be maximized. The objective is to find the transportation plan that generates the highest profit.