(x1, y1) = (1, 1), (x2, y2) = (3, 2), (x1, y1) = (4, 3)
Suppose that we want to determine a straight line with equation
. . . . .\(\displaystyle y\, =\, f(x)\, =\, ax\, +\, b\)
such that
. . . . .\(\displaystyle c\, =\, \mbox{max}\left\{|f(x_1)\, -\, y_1|,\, |f(x_2)\, -\, y_2|,\, |f(x_3)\, -\, y_3|\right\}\)
is as small as possible. Write down a linear programming model for determining the coefficients a and b.
It seems that question is asking for me to form a straight line that has the smallest gradient? But I kinda doubt this because we wouldn't need linear programming to do that, just a simple gradient calculator could do that.
So far all I can do is substitute each of the 3 coordinates to obtain
a+b=1
3a+b=2
4a+b=3
But this doesn't seem to make much sense.
Suppose that we want to determine a straight line with equation
. . . . .\(\displaystyle y\, =\, f(x)\, =\, ax\, +\, b\)
such that
. . . . .\(\displaystyle c\, =\, \mbox{max}\left\{|f(x_1)\, -\, y_1|,\, |f(x_2)\, -\, y_2|,\, |f(x_3)\, -\, y_3|\right\}\)
is as small as possible. Write down a linear programming model for determining the coefficients a and b.
It seems that question is asking for me to form a straight line that has the smallest gradient? But I kinda doubt this because we wouldn't need linear programming to do that, just a simple gradient calculator could do that.
So far all I can do is substitute each of the 3 coordinates to obtain
a+b=1
3a+b=2
4a+b=3
But this doesn't seem to make much sense.
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