By Eduard L. Stiefel (Auth.)
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Extra info for An Introduction to Numerical Mathematics
12). Let us now develop the table of the linear program (58) in the normal notation, where we take as objective function exactly that function ζ = χι + x2 which has to be made minimal: 36 2. 5 1 = ζ = (61) 0 Since the last row is positive, the table can be reduced by the simplex algorithm. We will take a look at the results of this process with no specific aim in mind at this time, other than general interest. 2, a row with a negative element in the last column must be selected as pivot row; we chose the third row.
In other words, Max must always use that strategy which is given by the saddle column; all other strategies are inactive. In the same way, Min always has to play the saddle row. Incidentally, the value of the game is equal to the saddle element. 7 Chebyshev Approximation A surveyor wants to measure the length of two adjoining segments A Β and BC of a straight line somewhere in a tract of land. Measuring each segment separately with a tape, he finds that A Β = 15 yards, BC = 6 yards. As a control, he also measures the entire line and finds that AC = 20 yards.
2. S O L U T I O N OF A PROGRAM W I T H T H E E X C H A N G E M E T H O D 25 condition that all variables y ι and xjc have to be positive: Vi > 0, xk> 0. Frequently it will also be required to minimize the objective function. This is nothing new because the problem ζ = min is equivalent to 11 (—z) - max. The use of equations as constraints can also be reduced to the above case. In fact, an equation y ι = 0 can be replaced by the two inequalities yi > 0 and (—yi) > 0. The formal scheme of this linear program has the form ...