In my book, the following rule for choosing a leaving variable is given:
$$x_k=\big(\max_{i\in B}\frac{\bar{a}_{ik}}{\bar{b}_i}\big)^{-1}$$
$$$$
But let us say you get the following scenario:
$$ratios_1 = \big(\frac{-3}{4}, \frac{-7}{3}, \frac{0}{0}\big)$$
What is the maximum of list of ratios? Is it $\frac{0}{0}$ ? How do I return the inverse of this?
The lets have another senario:
$$ratios_2 = \big(\frac{-3}{4}, \frac{1}{3}, \frac{3}{0}\big)$$
My book says that if the denominator vanishes,
"If the numerator is nonzero, then it is easy to see that the ratio should be interpreted as plus or minus infinity depending on the sign of the numerator".
So then the list should be:
$$ratios_2 = \big(\frac{-3}{4}, \frac{1}{3}, +\infty\big)$$
So the maximum of this list is $+\infty$. So, should I then take the inverse of infinity, how do I do so?
