Question 1

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.

Accepted Answer

The objective is $12 *30 + $9*70 + $ 7*60 + $15*90 +$8*50 = $3,160

Question 2

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

Accepted Answer

A)   The transportation model is at its ideal solution.
B)   The transportation model is at a feasible solution.
C)   The total cost saved by changing one unit on the route with an improvement index of 5 would be $5.
D)   The transportation matrix has four empty squares.
E)   Both B and D E

Question 3

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

Accepted Answer

A) True 
 B)False  True

Question 4

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?

Accepted Answer

The answer of Find the minimum cost solution for the...

Question 5

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

Accepted Answer

A)   the cost of shipping one unit from each origin to each destination
B)   the set of destinations and the demand at each
C)   the set of origins and the demand at each origin
D)   the list of sources and the capacity at each
E)   None of the above is needed.

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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?

Accepted Answer

A)   The problem will require a dummy demand with a capacity of 10 units.
B)   The problem is unbalanced and cannot be solved by the transportation method.
C)   The problem will require a dummy supply with a capacity of 10 units.
D)   Destinations C and D must each receive 5 units less than they require.
E)   None of the above is true.

Question 8

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?

Accepted Answer

A)   1 to 1
B)   2 to 2
C)   3 to 3
D)   4 to 3
E)   4 to 4

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

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.

Accepted Answer

A) True 
 B)False

Question 11

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?

Accepted Answer

The answer of A transportation model uses at least 10...

Question 12

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

Accepted Answer

A)   0
B)   15
C)   25
D)   45
E)   35

Question 13

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).

Accepted Answer

The answer of Given the following feasible solution determine if...

Question 14

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?

Accepted Answer

A)   2 sources, 4 destinations
B)   3 sources, 3 destinations
C)   4 sources, 2 destinations
D)   5 sources, 1 destination
E)   None of the above are degenerate.

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

The answer of A transportation model uses only 5% of...

Question 17

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.

Accepted Answer

A)   2
B)   13
C)   14
D)   48
E)   cannot be calculated without knowing the supply and demand totals

Question 18

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?

Accepted Answer

The answer of A transportation problem has 6 origins and...

Question 19

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.

Accepted Answer

The answer of Find the minimum cost solution for the...

Question 20

The stepping-stone method

Accepted Answer

A)   is an alternative to using the northwest-corner rule
B)   often involves tracing closed paths with a triangular shape
C)   is used to identify the relevant costs in a transportation problem
D)   is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution
E)   helps determine whether a solution is feasible or not

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.

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?

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