Problem $6$

Consider the following LP model and it's optimal simplex tableau:

MaxZ$=20x_1+8x_2$

$s.t.$

$5x_1+4x_{2}20$

$2x_1+5x_{2}11$

$x_1,x_{2}0$

a$.$ What's the impact of increasing an additional unit of resource $1$ and $2$ to the objective

function.

b$.$ If the range of coefficient in the objective function change to:

MaxZ$=(20-t)x_1^{\text{'}}+(8+t)x_2$

What is the range of $t,$ that the current optimal solution remains the same.