$2$ Question

Considering the following LP model, the corresponding optimal tableau and the sensitivity

report.

max$5x_1+10x_2+8x_3+4x_4$

$s.t.2x_1+2x_2+3x_3+x_{4}60$

$3x_1+4x_2+5x_{3}30$

$x_1+x_2+x_3+x_4=50$

$x_1,x_2,x_3,x_{4}0$

$B^{-1}=\left[\begin{array}{ccc}-1& 0& 2\\ A& -1& -4\\ 1& 0& -1\end{array}\right]$

Variable Cells

Answer the following questions by using the information provided above.

a$)$ Find the values of the $9$ unknowns A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G$,$ H$,$ I, J$,$ K$,$ L and N$.$ Explain how

you attain each.

b$)$ If you had the choice of increasing the RHS value of a single constraint by $1$ unit, which

constraint would you choose and why?

c$)$ How many units should the objective coefficient of $x_3$ increase such that there would be an

alternate optimal solution with $x_3$ in the basis? How would you determine this value from

the Excel output?

d$)$ What would happen when the RHS of constraint $1$ is decreased by $15$ units? If the optimality

gets disturbed, which feasibility would we determine and what would be the way to fix this

infeasibility?

e$)$ What is the optimal value and the optimal solution when the objective coefficient of $x_4$ is

increased by $4$ units? Answer also for the case where we increase the objective coefficient of

$x_3$ by $4$ units.

f$)$ Find the set of RHS values independently such that the current basis remains optimal.