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The solution to a transportation problem with ‘m’ rows (supplies) and ‘n’ columns (destination) is basically feasible if number of positive allocations are:a.m+nb.m*nc.m+n-1d.m+n+1

Question

The solution to a transportation problem with ‘m’ rows (supplies) and ‘n’ columns (destination) is basically feasible if number of positive allocations are:a.m+nb.m*nc.m+n-1d.m+n+1

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Solution

The solution to a transportation problem with 'm' rows (supplies) and 'n' columns (destinations) is basically feasible if the number of positive allocations are: m+n-1. So, the correct answer is c. m+n-1.

Here's the step by step explanation:

  1. In a transportation problem, we are trying to minimize the cost of transporting goods from several origins (supplies) to several destinations.

  2. Each origin has a supply capacity and each destination has a demand that needs to be met.

  3. A basic feasible solution of the transportation problem is an allocation of the supplies to the demands in such a way that the total supply equals the total demand.

  4. The number of positive allocations (i.e., allocations that are not zero) in a basic feasible solution is equal to the number of supplies plus the number of demands minus one (m+n-1).

  5. This is because each allocation represents a decision to transport goods from one origin to one destination. Since there are m origins and n destinations, there are m+n decisions to be made. However, since the total supply equals the total demand, one of these decisions is redundant and can be determined from the others. Hence, the number of independent decisions (or positive allocations) is m+n-1.

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