How to determine all the basic

How to determine all the basic solutions of an optimizationproblem, and classify them as feasible or infeasible?

As an example,

Maximize z= 2x1 + 3x2

Subject to:

x1 + 3x2 <= 6

3x1 + 2x2 <= 6

x1 + x2 >= 0

Some solutions are (2,0), (0,2), (0,0), (6/7, 12/7), but arethere more solutions? And how do you tell if they areinfeasile/feasible? Would you need to graph it?


The basic solutions are the solutions which solve any of theconstraints. However, feasible solutions are which satisfy allconstraints.So the basic solutions are all the points that lie on the lines

However out of this the feasible ones are that also satisfy theconstraints, so to do that find the intersecting points on thelines

X1 = 6/7

X2 = 22/7

So feasible solutions are the points that lie on either of theline but within the following range

So from our process above we find 4 points of interest. theseare actually the extreme points that satisfy our constraints. (Thiswill be a lot more clear in the graph)We have

(0,0), (0,2), (2,0), (6/7, 12/7)When we put all these points in the objective function, we findthat the maximum value occursat X2 = 12/7, X1 = 6/7 then z= 48/7we will just plot the graph and make things clear now

"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
Calculate the price
Make an order in advance and get the best price
Pages (550 words)
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Customer reviews in total
Current satisfaction rate
3 pages
Average paper length
Customers referred by a friend
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat

Sometimes it is hard to do all the work on your own

Let us help you get a good grade on your paper. Get professional help and free up your time for more important courses. Let us handle your;

  • Dissertations and Thesis
  • Essays
  • All Assignments

  • Research papers
  • Terms Papers
  • Online Classes