EXAMPle $5\mathrm{.}6\mathrm{.}1.$ DeChi, an electronics company, makes two gadgets

$($Models $1$ and $2)$ making use of resistors, capacitors and chips.

max$3x_1+4x_2$

$2x_1+3x_{2}1200(resistors)$

$2x_1+x_{2}1000(capacitors)$

$4x_{2}800(chips)$

$x_1,x_{2}0$

Optimal tableau:

Consider Example $5\mathrm{.}6\mathrm{.}1$ in Chapter $5.$ Suppose a new variable $x_3$ with coefficients $A_3=([-1],[2],[1])$ and

$c_3$ is added.

Determine the range of values for $c_3$ such that the current basic variables $(x_1,s_3,x_2)$ remain basic in

the optimal solution to the new LP$.$