Finite Math > Linear Programming > Simplex Minimums

The Dual | Nonstandard

Instructions

Shown on this page are youtube videos using a digital pen on virtual paper assisted by a HP Prime calculator emulator. The content found here extends the content found in our eBook or print copy of HP Prime Guide Algebra Fundamentals.

Click on play and the full screen option in the Embedded youtube video or click on the direct link to go directly to the youtube site to play the video.

Embedded youtube video displays a dialog window when we hit pause. Do not hit the “X’ to close the dialog window, just press the play icon or space bar to resume play as it closes the dialog window and resumes play.

Remark: Onenote Ink math assistant requires a 365 subscription. There is the personal 365 subscription,  academic 365 subscription with Class Notebooks for administrators, teachers, and students plus organizational versions of 365 subscriptions that include Onenote Ink math assistant. The videos were made using the academic 365 subscription. You will need a 365 subscription to duplicate the Onenote Ink math assistant parts, however there are free versions of Onenote for all platforms that include Ink but not the Ink math assistant. There is an Online Onenote broswer version available with the Onenote Ink math assistant for some subscription packages.


The Dual

The video uses the simplex method to solve minimum cost for a linear programming problem. We explore using the HP Prime catalog function simplex reduce and our function pivmat. Add pivmat(m,r,c):=CAS(pivot(CAS(mRow(1/m(r,c),m,r)),r,c)) to your calculator.  Go to 1:08 if you have pivmat already loaded. For matrices click the brackets key twice. For vectors click the brackets once. Use arrows key to enter elements in the command line. Use the brackets key twice or Matrix editor for M1.


HP Prime Onenote Simplex Standard Minimum or direct link

Simplex_reduce(Matrix A, Vector B. Vector C) gives optimum maximum for the Dual problem by using the simplex algorithm on HP Prime for standard linear programming problems. Pivmat(Matrix, Pivot Row, Pivot Column) gives column information for a pivot element to allow us to manually solve the Dual problem.

Microsoft is in the process of adding equation editor to 365 subscription of Onenote for Windows 10. They recommend you use equation editor in Word and copy and paste into Onenote for Windows 10. That is what we did to get the less than equal symbol.


Nonstandard

Video shows us calculating the minimum C by using P = - C and using the related maximum P problem. All >= are changed to <= inequalites. The equality is changed to two <= inequalities. We use pivmat function to find a feasible, starting vertex, for simplex_reduce.

The video uses the simplex method to solve minimum cost for a linear programming problem. We explore using the HP Prime catalog function simplex reduce and our function pivmat. Add pivmat(m,r,c):=CAS(pivot(CAS(mRow(1/m(r,c),m,r)),r,c)) to your calculator.  Go to 1:08 if you have pivmat already loaded. For matrices click the brackets key twice. For vectors click the brackets once. Use arrows key to enter elements in the command line. Use the brackets key twice or Matrix editor for M1.


HP Prime Onenote Simplex Nonstandard Minimum or direct link

Simplex_reduce(Matrix A, Vector B. Vector C) gives optimum maximum for maximum problems by using the simplex algorithm on HP Prime for standard linear programming problems. Pivmat(Matrix, Pivot Row, Pivot Column) gives column information for a pivot element to allow us to manually solve the maximum problem. For nonstandard maximum problems pivmat allows us to come up with a feasible solution. This feasible solution tableau, matrix, can then be the sole argument for Simplex_reduce. We initially use P = - C and for the last step use C = - P.

A special case for <= constraints that are all positive. We can use simplex_reduce(Matrix A, Vector B. Vector) or simplex_reduce(Matrux) directly with the related P maximum problem

Microsoft is in the process of adding equation editor to 365 subscription of Onenote for Windows 10. They recommend you use equation editor in Word and copy and paste into Onenote for Windows 10. That is what we did to get the less than equal symbol.


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