Texas Instruments TI-89 and TI-92 Plus Computer 

Last page update: December 21, 1999 
Lagrange Optimization Function - for the TI-89 and TI-92 Plus
Version 1.1   (December 16, 1999)
Download [ lagrange.zip]
Description Uses Lagrange Multipliers for optimization. 
1.1: Modified function to allow easy language translation. see <language.html>.
Screen shots
Screen image
Documentation Usage:

ObjectiveExpr: The objective function.

ConstraintExpr: The constraint expression or a list of constraint expressions. Does not need to be a list if there is only one constraint.

ConstraintVal: The value of the constraint expression. This must be zero if the value has already been subtracted from the constraint expression. For example: lagrange(x+y, x2+y2, 1, {x,y}) or lagrange(x+y, x2+y2-1, 0, {x,y}). Does not need to be a list if there is only one constraint.

VarList: The list of variables in the functions. 

Return value:
A matrix where each row of the matrix is a solution. The last column of the matrix is ObjectiveExpr evaluated at the point specified by the preceding columns. 

1. Find the maximum and minimum values of x+y subject to the constraint x2+y2=1:
   lagrange( x+y, x2+y2, 1, {x,y})
    [[sqrt(2)/2,   sqrt(2)/2,  sqrt(2)]
     [-sqrt(2)/2, -sqrt(2)/2, -sqrt(2)]]

  Row 1: x =  sqrt(2)/2,   y =  sqrt(2)/2,  x+y =  sqrt(2)  Maximum
  Row 2: x = -sqrt(2)/2,   y = -sqrt(2)/2,  x+y = -sqrt(2)  Minimum