Linear Programming using Microsoft Solver

  

Consider the following example that demonstrates optimization of transportation.

There are production facilities in Battle Creek, Cherry Creek, and Dee Creek with annual capacities of 500 units, 400 units, and 600 units, respectively. The annual demands at warehouses in Worchester, Dorchester, and Rochester are 300 units, 700 units, and 400 units, respectively. The table below gives the unit transportation costs between the production facilities and the warehouses. Worchester

Don't use plagiarized sources. Get Your Custom Essay on
Linear Programming using Microsoft Solver
Just from $13/Page
Order Essay

Dorchester

Rochester

Battle Creek

$20/unit

$30/unit

$13/unit

Cherry Creek

$10/unit

$5/unit

$17/unit

Dee Creek

$15/unit

$12/unit

$45/unit

This problem can be modeled as a linear programming model as follows:
Decision Variables
Xbw = # of units to be transported from Battle Creek to Worchester
Xcw = # of units to be transported from Cherry Creek to Worchester
Xdw = # of units to be transported from Dee Creek to Worchester
Xbd = # of units to be transported from Battle Creek to Dorchester
Xcd = # of units to be transported from Cherry Creek to Dorchester
Xdd = # of units to be transported from Dee Creek to Dorchester Xbr = # of units to be transported from Battle Creek to Rochester
Xcr = # of units to be transported from Cherry Creek to Rochester
Xdr = # of units to be transported from Dee Creek to Rochester
Objective Function
Minimize total annual transportation cost ($):
= 20*Xbw + 10*Xcw + 15*Xdw + 30*Xbd + 5*Xcd + 12*Xdd + 13*Xbr + 17*Xcr + 45*Xdr
Constraints
Demand Constraints
Xbw + Xcw + Xdw = 300 (demand at Worchester)
Xbd + Xcd + Xdd = 700 (demand at Dorchester)
Xbr + Xcr + Xdr = 400 (demand at Rochester)
Capacity Constraints
Xbw + Xbd + Xbr = 500 (capacity at Battle Creek)
Xcw + Xcd + Xcr = 400 (capacity at Cherry Creek)
Xdw + Xdd + Xdr = 600 (capacity at Dee Creek)
Non-Negativity Constraints
Xbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are = 0
Integer Constraints
Xbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are integers
The above model can be solved using the Microsoft Excel Solver tool.

  
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more