Question

9-7 The management of the Executive Furniture Corporation decided to expand the production capacity at its...

9-7 The management of the Executive Furniture Corporation decided to expand the production capacity at its Des Moines factory and to cut back the production capacities at its other two factories. It also recognizes a shifting market for its desks and revises the requirements at its three warehouses.

The table on this page provides the requirement at each of the warehouses, the capacity at each of the factories, and the shipping cost per unit to ship from each factory to each warehouse. Find the least-cost way to meet the requirements given the capacity at each factory.

TO FROM ALBUQUERQUE BOSTON CLEVELAND CAPACITY
DES MOINES $5 $4 $3 300
EVANSVILLE $8 $4 $3 150
FORT LAUDERDALE $9 $7 $5 250
REQUIREMENTS 200 200 300

Could you show me how to formulate and how the Excel should look like as well?

Thank you!

0 0
Add a comment Improve this question Transcribed image text
Answer #1

We formulate the problem as shown:

Let the units shipped from Des Moines to Albuquerque be x11, Des Moines to Boston be x12 and so on

We get the decision variables as shown below:

TO FROM DES MOINES EVANSVILLE FORT LAUDERDALE REQUIREMENTS ALBUQUERQUE BOSTON CLEVELAND CAPACITY x11 x12 x13 300 x22 x23 150

Total cost of shipping will be product of shipping cost per unit * corresponding shipped unit

Total cost = 5*x11 + 4*x12 + 3*x13 + 8*x21 + 4*x22 + 3*x23 + 9*x31 + 7*x32 + 5*x33

We have to minimize this cost

We get constraints on capacity and requirements from table as shown:

x11 + x12 + x13 = 300..........Total Capacity for Des Moines

x21 + x22 + x23 = 150..........Total Capacity for Evansville

x31 + x32 + x33 = 250..........Total Capacity for Fort Lauderdale

x11 + x21 + x31 = 200..........Total Requirement for Albuquerque

x12 + x22 + x32 = 200..........Total Requirement for Boston

x13 + x23 + x33 = 300..........Total Requirement for Cleveland

All quantities are non-negative.

Hence, we get formulation as:

Minimize total cost z = 5*x11 + 4*x12 + 3*x13 + 8*x21 + 4*x22 + 3*x23 + 9*x31 + 7*x32 + 5*x33

Subject to constraints:

x11 + x12 + x13 = 300

x21 + x22 + x23 = 150

x31 + x32 + x33 = 250

x11 + x21 + x31 = 200

x12 + x22 + x32 = 200

x13 + x23 + x33 = 300

x11, x12, x13, x21, x22, x23, x31, x32, x33 >= 0

We solve the given problem in excel as shown below. We tabulate the data in excel as shown:

1 TO FROM 2 DES MOINES 3 EVANSVILLE 4 FORT LAUDERDALE 5 REQUIREMENTS ALBUQUERQUE BOSTON CLEVELAND CAPACITY $ 5 $ 4 $ 3 300 $

Since the capacity and requirements are same, it is a balanced transportation problem

We prepare the excel tables as follows using relevant formulas for requirement, capacity and total costs

А 1 TO FROM 2 DES MOINES 3 EVANSVILLE 4 FORT LAUDERDALE 5 REQUIREMENTS ALBUQUERQUE BOSTON CLEVELAND CAPACITY 5 $ 4 $ 3 300 8

The above tables in form of formulas are shown below:

ALBUQUERQUE BOSTON CLEVELAND A 1 TO FROM 2 DES MOINES 3 EVANSVILLE 4 FORT LAUDERDALE 5 REQUIREMENTS CAPACITY 300 150 250 =SUM

We solve the given problem in excel solver as follows:

A 1 TO FROM ALBUQUERQUE BOSTON CLEVELAND CAPACITY 2 DES MOINES $ 5 $ 4 $ 3 300 3 EVANSVILLE $ 8 $ 4 $ 3 150 4 FORT LAUDERDALE

The above solution with excel solver extract is shown below:

M N O Solver Parameters X 1 TO FROM 2 DES MOINES 3 EVANSVILLE 4 FORT LAUDERDALE 5 REQUIREMENTS 1 ALBUQUERQUE BOSTON CLEVELAND

The above-shown solution under the table Variable is the least cost way for shipping the units.

Add a comment
Know the answer?
Add Answer to:
9-7 The management of the Executive Furniture Corporation decided to expand the production capacity at its...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 9-7 The management of the Executive Furniture Corpo- ration decided to expand the production capacity at...

    9-7 The management of the Executive Furniture Corpo- ration decided to expand the production capacity at its Des Moines factory and to cut back the produc- tion capacities at its other two factories. It also rec- ognizes a shifting market for its desks and revises the requirements at its three warehouses. The table on this page provides the requirement at each of the warehouses, the capacity at each of the factories, and the shipping cost per unit to ship from...

  • There are three factories producing bath tubs have capacities as follows - Des Monies 100 tubs...

    There are three factories producing bath tubs have capacities as follows - Des Monies 100 tubs per day - Evansville 300 tubs per day - Fort Lauderdale 300 tubs per day These tubs need to be shipped to three warehouses whose demands are as follows - Albuquerque 300 tubs per day - Boston 200 tubs per day - Cleveland 200 tubs per day. Cost of shipping one tub from each factory to each warehouse are as follows Des Monies to...

  • Show Work ABC Corporation has three plants with production capacity and plans to begin a production...

    Show Work ABC Corporation has three plants with production capacity and plans to begin a production of a product that can be made in three sizes – large, medium and small – that yield a net unit profit of $420, $360 and $300 respectively. Plants 1, 2 and 3 have capacity to produce 750, 900, and 450 units per day of this product, respectively, regardless of the size or combination of sizes involved. The amount of available storage space also...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT