If the simplex iterations start at point A$,$ identify the path to the optimum point E$.$

Determine the entering variable, the corresponding ratios of the feasibility condition, and the change in the value of z$,$ assuming that the starting iteration occurs at point A and that the objective function is given as

Maximize

$$

z

$=$

$4$

x

$1$

$+$

x

$2$

Repeat $($b$),$ assuming that the objective function is

Maximize

$$

z

$=$

x

$1$

$+$

$4$

x

$2$