Question 1

Solve the following transportation problem using the transportation simplex method. State the minimum total shipping cost. $$\begin{array} { c c | c c } 
\text { Origin } & \text { Supply } & \text { Destination } & \text { Demand } \
\hline \text { A } & 500 & \mathrm { X } & 300 \
\mathrm {~B} & 400 & \mathrm { Y } & 300 \
& & \mathrm { Z } & 300
\end{array}$$ Shipping costs are: $$\begin{array} { c | c c c } 
&& { \text { Destination } } \
\text { Source } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \
\hline \mathrm { A } & 2 & 3 & 5 \
\mathrm {~B} & 9 & 12 & 10
\end{array}$$

Accepted Answer

The answer of Solve the following transportation problem using the...

Question 2

The following table shows the unit shipping cost between cities, the supply at each origin city, and the demand at each destination city. Solve this minimization problem using the transportation simplex method and compute the optimal total cost. $$\begin{array} { l | c c c c | c } 
&&&{ \text { Destination } } & \
\text { Origin } & \text { Terre Haute } & \text { Indianapolis } & \text { Ft. Wayne } & \text { South Bend } & \text { Supply } \
\hline \text { St. Louis } & 8 & 6 & 12 & 9 & 100 \
\text { Evansville } & 5 & 5 & 10 & 8 & 100 \
\text { Bloomington } & 3 & 2 & 9 & 10 & 100 \
\hline \text { Demand } & 150 & 60 & 45 & 45 &
\end{array}$$

Accepted Answer

The answer of The following table shows the unit shipping...

Question 3

Five customers needing their tax returns prepared must be assigned to five tax accountants. The estimated profits for all possible assignments are shown below. Only one accountant can be assigned to a customer, and all customers' tax returns must be prepared. What should the customer-accountant assignments be so that estimated total profit is maximized? What is the resulting total profit? $$\begin{array} { c r r r r r } 
&&&\text { Accountant }\
\text { Customer } & 1 & 2 & 3 & 4 & 5 \
\hline \text { A } & \$ 500 & \$ 525 & \$ 550 & \$ 600 & \$ 700 \
\text { B } & 625 & 575 & 700 & 550 & 800 \
\text { C } & 825 & 650 & 450 & 750 & 775 \
\text { D } & 590 & 650 & 525 & 690 & 750 \
\text { E } & 450 & 750 & 660 & 390 & 550 \
\hline
\end{array}$$

Accepted Answer

The answer of Five customers needing their tax returns prepared...

Question 4

A professor has been contacted by four not-for-profit agencies that are willing to work with student consulting teams. The agencies need help with such things as budgeting, information systems, coordinating volunteers, and forecasting. Although each of the four student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. The professor's estimate of the time, in days, is given in the table below. Use the Hungarian method to determine which team works with which project. All projects must be assigned and no team can be assigned to more than one project. $$\begin{array} { c | c c c c } 
& & { \text { Projects } } \
\text { Team } & \text { Budgeting } & \text { Information } & \text { Volunteers } & \text { Forecasting } \
\hline \text { A } & 32 & 35 & 15 & 27 \
\text { B } & 38 & 40 & 18 & 35 \
\text { C } & 41 & 42 & 25 & 38 \
\text { D } & 45 & 45 & 30 & 42
\end{array}$$

Accepted Answer

The answer of A professor has been contacted by four...

Question 5

Consider the transportation problem below. $$\begin{array}{l}
\text { Destination }\
\begin{array} { c r r r c } 
\text { Origin } &  { 1 } & { 2 } & { 3 } & \text { Supply } \
\hline \text { A } & \$ .50 & \$ .90 & \$ .50 & 100 \
\text { B } & .80 & 1.00 & .40 & 500 \
\text { C } & .90 & .70 & .80 & 900 \
\hline \text { Demand } & 300 & 800 & 400 &
\end{array}
\end{array}$$ 
a.Use the minimum cost method to find an initial feasible solution.
b.Can the initial solution be improved?
c.Compute the optimal total shipping cost.

Accepted Answer

The answer of Consider the transportation problem below. \[\begin{array}{l}
\text {...

Question 6

Use the Hungarian method to obtain the optimal solution to the following assignment problem in which total cost is to be minimized. All tasks must be assigned and no agent can be assigned to more than one task. $$\begin{array} { c | c c c c } 
& & { \text { Task } } \
\text { Agent } & \text { A } & \text { B } & \text { C } & \text { D } \
\hline 1 & 10 & 12 & 15 & 25 \
2 & 11 & 14 & 19 & 32 \
3 & 18 & 21 & 23 & 29 \
4 & 15 & 20 & 26 & 28
\end{array}$$

Accepted Answer

The answer of Use the Hungarian method to obtain the...

Question 7

To handle unacceptable routes in a transportation problem where cost is to be minimized, infeasible arcs must be assigned negative cost values.

Accepted Answer

Infeasible arcs in a transportation problem are assigned a very high cost (not negative) to ensure they are not selected in the solution. Negative costs would encourage their selection, which is contrary to the goal of avoiding these routes.

Question 8

Al Bergman, staff traffic analyst at the corporate headquarters of Computer Products Corporation (CPC), is developing a monthly shipping plan for the El Paso and Atlanta manufacturing plants to follow next year. These plants manufacture specialized computer workstations that are shipped to five regional warehouses. Al has developed these estimated requirements and costs: $$\begin{array} { l c r r r r r } 
&&&  { \text { Warehouse } } \
\text { Plant } & \text { Chicago } & \text { Dallas } & \text { Denver } & \begin{array} { c } 
\text { New } \
\text { York }
\end{array} & \text { San Jose } & \begin{array} { c } 
\text { Monthly Plant } \
\text { Production (units) }
\end{array} \
\hline \text { Atlanta } & \$ 35 & \$ 40 & \$ 60 & \$ 45 & \$ 90 & 200 \
\text { El Paso } & 50 & 30 & 35 & 95 & 40 & 300 \
\hline \begin{array} { l } 
\text { Monthly } \
\text { Warehouse }
\end{array} & & & & & & \
\begin{array} { l } 
\text { Requirements } \
\text { (units) }
\end{array} & 75 & 100 & 25 & 150 & 150
\end{array}$$ Determine how many workstations should be shipped per month from each plant to each warehouse to minimize monthly shipping costs, and compute the total shipping cost. 
a.Use the minimum cost method to find an initial feasible solution.
b.Use the transportation simplex method to find an optimal solution.
c.Compute the optimal total shipping cost.

Accepted Answer

The answer of Al Bergman, staff traffic analyst at the...

Question 9

Explain how the Hungarian method can be used to solve an assignment problem that has a maximization objective.

Accepted Answer

The answer of Explain how the Hungarian method can be...

Question 10

Using the Hungarian method, the optimal solution to an assignment problem is found when the minimum number of lines required to cover the zero cells in the reduced matrix equals the number of agents.

Accepted Answer

This statement is true. The Hungarian method involves using a reduced matrix to find the optimal solution to an assignment problem. The minimum number of lines that need to be drawn to cover all the zero cells in the reduced matrix is equal to the number of agents involved in the problem. Once this condition is met, the optimal solution can be found by assigning each agent to the task that corresponds to the uncovered zero cell in their row or column.

Question 11

A manufacturer of electrical consumer products, with its headquarters in Burlington, Iowa, produces electric irons at Manufacturing Plants 1, 2, and 3. The irons are shipped to Warehouses A, B, C, and D. The shipping cost per iron, the monthly warehouse requirements, and the monthly plant production levels are: $\begin{array}{lccccc} 
&&\text { Thatehouse }&&&\text { Monthly Plant }\
& \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \text { Froduction (units) } \
\hline \text { Plant 1 } & \$ .20 & \$ .25 & \$ .15 & \$ .20 & 10,000 \
\text { Plant 2 } & .15 & .30 & .20 & .15 & 20,000 \
\text { Plant 3 } & .15 & .20 & .20 & .25 & 10,000\\hline
\text { Monthly Warehouse } & 12,000 & 8,000 & 15,000 & 5,000 \
\text { Requirements (units) }\
\end{array}$ How many electric irons should be shipped per month from each plant to each warehouse to minimize monthly shipping costs? 
a.Use the minimum cost method to find an initial feasible solution.
b.Can the initial solution be improved?
c.Compute the optimal total shipping cost per month.

Accepted Answer

The answer of A manufacturer of electrical consumer products, with...

Question 12

For an assignment problem where the number of agents does not equal the number of tasks, what adjustments must be made to allow the problem to be solved using the Hungarian method?

Accepted Answer

The answer of For an assignment problem where the number...

Question 13

Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a 0.

Accepted Answer

The Hungarian method uses the 0s in the reduced matrix to make optimal assignments.

Question 14

Explain what adjustments are made to the transportation tableau when there are unacceptable routes.

Accepted Answer

The answer of Explain what adjustments are made to the...

Question 15

Canning Transport is to move goods from three factories (origins) to three distribution centers (destinations). Information about the move is given below. Solve the problem using the transportation simplex method and compute the total shipping cost. $$\begin{array} { c c | c c } 
\text { Origin } & \text { Sapply } & \text { Destination } & \text { Denand } \
\hline \text { A } & 200 & \mathrm { X } & 50 \
\mathrm {~B} & 100 & \mathrm { Y } & 125 \
\mathrm { C } & 150 & \mathrm { Z } & 125
\end{array}$$ Shipping costs are: $$\begin{array}{l}
\begin{array} { c | c c c } 
&& { \text { Destination } } \
\text { Origin } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \
\hline \mathrm { A } & 3 & 2 & 5 \
\mathrm {~B} & 9 & 10 & - \
\mathrm { C } & 5 & 6 & 4
\end{array}\
\text { (Source B cannot ship to destination Z) }
\end{array}$$

Accepted Answer

The answer of Canning Transport is to move goods from...

Question 16

Solve the following assignment problem using the Hungarian method. No agent can be assigned to more than one task. Total cost is to be minimized. $$\begin{array} { c | r r c c } 
&& { \text { Task } } \
\text { Agent } & \text { A } & \text { B } & \text { C } & \text { D } \
\hline 1 & 9 & 5 & 4 & 2 \
2 & 12 & 6 & 3 & 5 \
3 & 11 & 6 & 5 & 7
\end{array}$$

Accepted Answer

The answer of Solve the following assignment problem using the...

Question 17

Explain what adjustments are made to the transportation tableau when total supply and total demand are not equal.

Accepted Answer

The answer of Explain what adjustments are made to the...

Question 18

Explain how the transportation simplex method can be used to solve a transportation problem that has a maximization objective.

Accepted Answer

The answer of Explain how the transportation simplex method can...

Question 19

After some special presentations, the employees of the AV Center have to move overhead projectors back to classrooms. The table below indicates the buildings where the projectors are now (the origins), where they need to go (the destinations), and a measure of the distance between sites. Determine the transport arrangement that minimizes the total transport distance. $$\begin{array} { l | c c c c | c } 
& && { \text { Destination } } & \
\text { Origin } & \text { Business } & \text { Education } & \text { Parsons Hall } & \text { Holmstedt Hall } & \text { Supply } \
\hline \text { Baker Hall } & 10 & 9 & 5 & 2 & 35 \
\text { Tirey Hall } & 12 & 11 & 1 & 6 & 10 \
\text { Arena } & 15 & 14 & 7 & 6 & 20 \
\hline \text { Dem and } & 12 & 20 & 10 & 10 &
\end{array}$$

Accepted Answer

The answer of After some special presentations, the employees of...

Question 20

Develop the transportation tableau for this transportation problem.

Accepted Answer

The answer of Develop the transportation tableau for this transportation...

Quiz 19: Solution Procedures for Transportation and Assignment Problems