Exam 20: The Simplex Method of Linear Programming

Consider the transportation problem in the data set and optimal solution below. Verify by hand or by calculator (show your work) the value of the objective function.

A transportation problem has improvement indices of 5, 4, 0, and -3. Which of the following is always true?

In a transportation minimization problem, the negative improvement index associated with a cell indicates that reallocating units to that cell would lower costs.

Find the minimum cost solution for the transportation problem detailed in the table below. Before your solution can be implemented, you discover that the combination Source 3 - Destination 1 is unavailable, due to political turmoil in the country where Source 3 is located. Solve the revised problem. How much is cost increased by this complication?

Which of the following is not information needed for a transportation problem?

The stepping-stone method frequently achieves an optimal solution as soon as it calculates an initial feasible solution.

A transportation problem has two origins: A can supply 20 units and B can supply 30 units. This problem has two destinations: C requires 25 units and D requires 35 units. Which of the following is true?

A transportation model fills one-half of its cells under the optimal solution. Which of the following most closely describes the number of sources compared to the number of destinations?

Neither the northwest corner rule nor the intuitive method considers shipping cost in making initial allocations.

The transportation model is an excellent tool for minimizing shipping costs among existing facilities, but it is not useful when firms consider new facility locations.

A transportation model uses at least 10 sources and 100 destinations. If the ratio of sources to destinations remains constant, does the maximum % of cells used by the optimum solution remain constant? Why or why not?

For the problem data set below, what is the northwest corner allocation to the cell Source 1 -Destination 2?

Given the following feasible solution determine if the problem is degenerate and then find the optimal solution and its cost. Assume that capacity for source A is 10 and 30 for source B. Destination A demands 10 units while destination B demands 30 units. Cost of shipping per unit is given as AA ($4), AB ($1), BA ($3), and BB ($2).

Suppose the solution for a transportation model fills 5 cells with quantities to be shipped. Which of the following combinations of sources and destinations would be degenerate?

To handle degeneracy, a very small quantity is placed in one of the unused squares.

A transportation model uses only 5% of its cells. If the number of destinations is 1000, determine the number of sources in the model.

A transportation problem has 8 origins and 6 destinations. The optimal solution of this problem will fill no more than __________ cells with quantities to be shipped.

A transportation problem has 6 origins and 12 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

Find the minimum cost solution for the transportation problem detailed in the table below. Explain carefully the meaning of any quantity in a "dummy" row or column.

The stepping-stone method