2 The algorithm gives a method for drawing two straight lines, if certain conditions are met. Start with the equations of the two straight lines
Line 1 is \(a x + b y = c , \quad a , b , c > 0\)
Line 2 is \(d x + e y = f , \quad d , e , f > 0\)
Let \(X =\) minimum of \(\frac { c } { a }\) and \(\frac { f } { d }\)
Let \(Y =\) minimum of \(\frac { c } { b }\) and \(\frac { f } { e }\) If \(X = \frac { c } { a }\) then \(X ^ { * } = \frac { c - b Y } { a }\) and \(Y ^ { * } = \frac { f - d X } { e }\) If \(X = \frac { f } { d }\) then \(X ^ { * } = \frac { f - e Y } { d }\) and \(Y ^ { * } = \frac { c - a X } { b }\)
Draw an \(x\)-axis labelled from 0 to \(X\), and a \(y\)-axis labelled from 0 to \(Y\)
Join ( \(0 , Y\) ) to ( \(X , Y ^ { * }\) ) with a straight line
Join ( \(X ^ { * } , Y\) ) to ( \(X , 0\) ) with a straight line

1. Apply the algorithm with \(a = 1 , b = 5 , c = 25 , d = 10 , e = 2 , f = 85\).
2. Why might this algorithm be useful in an LP question?