Question 1

Upon completion of the northwest-corner rule, which source-destination cell is guaranteed to be occupied?
A) top-left
B) top-right
C) bottom-left
D) bottom-right
E) the cell with the lowest shipping cost (or at least one of them if there's a tie)

Accepted Answer

The northwest-corner rule always starts filling the table from the top-left cell and moves to the right and down. Therefore, the top-left cell is guaranteed to be occupied.

Question 2

The Northwest-Corner rule's biggest flaw is that
A) it ignores costs
B) it cannot generate feasible solutions
C) it never generates ideal solutions
D) it ignores shipping time
E) There are no major flaws.

Accepted Answer

The Northwest-Corner rule only considers the quantity of goods to be transported between sources and destinations, and does not take into account the costs involved in transporting those goods. This can result in inefficient and costly solutions.

Question 3

Consider the transportation problem and its optimal solution in the tables below. What is the value of the objective function? 
A) 0
B) $169
C) 300 units
D) $2,100
E) $3,140

Accepted Answer

The answer of Consider the transportation problem and its optimal...

Question 4

Consider the transportation problem and its optimal solution in the tables below. The cell Source 3 - Destination 3 is currently empty. What would be the change in the objective function if the largest possible amount were shipped using that route, leaving all the supply and demand conditions unchanged? 
A) 0
B) fifty units
C) a decrease of $9
D) an increase of $450
E) an increase of $630

Accepted Answer

If the largest possible amount were shipped using the empty route, which is 50 units, the objective function value would increase by $450.

To calculate this, we first need to determine the cost per unit of shipping on that route, which is $9. We then multiply that by the quantity shipped (50), resulting in an increase of $450.

Question 5

A transportation problem has a feasible solution when
A) all of the improvement indices are greater than or equal to zero
B) all demand and supply constraints are satisfied
C) the number of filled cells is one less than the number of rows plus the number of columns
D) all the squares are used
E) the solution yields the lowest possible cost

Accepted Answer

A transportation problem has a feasible solution when all demand and supply constraints are satisfied, meaning that the total supply of goods equals the total demand for goods. The other options describe conditions that may be necessary for an optimal solution, but not for a feasible solution.

Question 6

For the problem data set below, what is the northwest corner allocation to the cell Source 3-Destination 3? 
A) 0
B) 15
C) 20
D) 35
E) 45

Accepted Answer

The answer of For the problem data set below, what...

Question 7

For the problem data set below, what is the northwest corner allocation to the cell Source 1 -Destination 2? 
A) 0
B) 15
C) 25
D) 45
E) 35

Accepted Answer

The answer of For the problem data set below, what...

Question 8

The purpose of the transportation approach for location analysis is to minimize
A) total costs
B) total variable costs
C) total fixed costs
D) total shipping costs
E) the number of shipments

Accepted Answer

The transportation approach involves finding the optimal shipping plan that minimizes the total shipping costs from suppliers to the facility and from the facility to customers. Therefore, the purpose of the transportation approach is to minimize the total shipping costs.

Question 9

A transportation problem has an optimal solution when
A) all of the improvement indices are greater than or equal to zero
B) all demand and supply constraints are satisfied
C) the number of filled cells is one less than the number of rows plus the number of columns
D) all the squares are used
E) all origin-destination combinations have been made equally low in cost

Accepted Answer

The answer of A transportation problem has an optimal solution...

Question 10

The initial solution to a transportation problem can be generated several ways, so long as
A) it minimizes cost
B) it ignores cost
C) all supply and demand conditions are satisfied
D) degeneracy does not exist
E) all cells are filled

Accepted Answer

The initial solution should satisfy all supply and demand conditions. This means that all sources must have their demands fulfilled and all destinations must receive the required amounts. The other options listed do not guarantee the satisfaction of all supply and demand conditions.

Question 11

In a minimization problem, a negative improvement index in a cell indicates that the
A) solution is optimal
B) total cost will increase if units are reallocated to that cell
C) current iteration is worse than the previous one
D) total cost will decrease if units are reallocated to that cell
E) problem has no feasible solution

Accepted Answer

A negative improvement index in a cell indicates that the total cost will decrease if units are reallocated to that cell, hence making it a better solution than the current one.

Question 12

For the problem data set below, what is the northwest corner allocation to the cell Source 1-Destination 1? 
A) 0
B) 2
C) 15
D) 90
E) 30

Accepted Answer

The northwest corner method starts with allocating the largest possible amount to the cell in the top left corner and then working downwards and to the right. In this case, the largest amount that can be allocated to the cell Source 1-Destination 1 is the minimum of the supply at Source 1 (15) and the demand at Destination 1 (20), which is 15. Therefore, the answer is C: 15.

Question 13

For the problem below, what is the quantity assigned to the cell Source 3-Destination 1 using the intuitive method for an initial feasible solution? 
A) 3
B) 13.333
C) 30
D) 45
E) 50

Accepted Answer

The answer of For the problem below, what is the...

Question 14

For the problem below, what is the quantity assigned to the cell Source 1-Destination 2 using the intuitive method for an initial feasible solution? 
A) 1
B) 5
C) 30
D) 45
E) 50

Accepted Answer

The answer of For the problem below, what is the...

Question 15

In transportation model analysis the stepping-stone method is used to
A) obtain an initial optimum solution
B) obtain an initial feasible solution
C) evaluate empty cells for possible degeneracy
D) balance supply and demand
E) evaluate empty cells for potential solution improvements

Accepted Answer

The stepping-stone method is used to improve the initial feasible solution by evaluating empty cells for potential solution improvements. It involves testing the potential improvement in the objective function value when a unit of flow is added to or subtracted from an empty cell. This process is repeated until no further improvements can be made. It does not obtain an initial feasible or optimum solution, balance supply and demand, or evaluate empty cells for degeneracy.

Question 16

The main difference between the intuitive lowest-cost method and the Northwest-corner rule is that
A) the intuitive lowest-cost method always generates a better solution
B) the Northwest-corner rule is faster
C) the Northwest-corner rule ignores cost
D) only the intuitive lowest-cost method generates an optimal solution
E) None of the above are accurate.

Accepted Answer

The answer of The main difference between the intuitive lowest-cost...

Question 17

The northwest-corner rule is best used
A) to minimize the total shipping cost from several origins to several destinations
B) to calculate whether a feasible solution is also an optimal solution
C) to calculate how much to transfer from one shipping route to another
D) to generate an initial feasible solution to a transportation problem
E) to resolve cases of degeneracy in transportation problems

Accepted Answer

The northwest-corner rule is a method to generate an initial feasible solution to a transportation problem. It involves allocating shipments starting from the top-left corner of the tableau until either the supply or demand of a particular source or destination is satisfied. This method is not suitable for minimizing total shipping cost, calculating optimality, or resolving degeneracy.

Question 18

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

Accepted Answer

The answer of Which of the following is not information...

Question 19

The transportation method is a special case of the family of problems known as
A) regression problems
B) decision tree problems
C) linear programming problems
D) simulation problems
E) statistical problems

Accepted Answer

The transportation problem is a type of linear programming problem that involves finding the optimal way to transport goods from sources to destinations. Linear programming is a mathematical method used to determine the best possible solution to a problem that requires linear relationships between variables.

Question 20

The total cost of the optimal solution to a transportation problem
A) is calculated by multiplying the total supply (including any dummy values) by the average cost of the cells
B) cannot be calculated from the information given
C) can be calculated based only on the entries in the filled cells of the solution
D) can be calculated from the original northwest corner solution
E) is found by multiplying the amounts in each cell by the cost for that cell for each row and then subtracting the products of the amounts in each cell times the cost of each cell for the columns

Accepted Answer

The total cost of the optimal solution to a transportation problem is calculated by multiplying the amounts in each filled cell by the cost for that cell and summing these products. This method directly uses the entries in the filled cells of the solution, which represent the quantities to be transported and their respective costs.

Quiz 20: The Simplex Method of Linear Programming

Upon completion of the northwest-corner rule, which source-destination cell is guaranteed to be occupied?

The Northwest-Corner rule's biggest flaw is that

Consider the transportation problem and its optimal solution in the tables below. What is the value of the objective function?

A transportation problem has a feasible solution when

For the problem data set below, what is the northwest corner allocation to the cell Source 3-Destination 3?

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

The purpose of the transportation approach for location analysis is to minimize

A transportation problem has an optimal solution when

The initial solution to a transportation problem can be generated several ways, so long as

In a minimization problem, a negative improvement index in a cell indicates that the

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

For the problem below, what is the quantity assigned to the cell Source 3-Destination 1 using the intuitive method for an initial feasible solution?

For the problem below, what is the quantity assigned to the cell Source 1-Destination 2 using the intuitive method for an initial feasible solution?

In transportation model analysis the stepping-stone method is used to

The main difference between the intuitive lowest-cost method and the Northwest-corner rule is that

The northwest-corner rule is best used

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

The transportation method is a special case of the family of problems known as

The total cost of the optimal solution to a transportation problem