LINDO Output Is Given for the Following Linear Programming Problem

question 11

Essay

LINDO output is given for the following linear programming problem.
MIN
12 X1 + 10 X2 + 9 X3
SUBJECT TO
2) 5 X1 + 8 X2 + 5 X3 > = 60
3) 8 X1 + 10 X2 + 5 X3 > = 80
END
LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1) 80.000000 $$\begin{array} { c c c } \text { VARIABLE } & \text { VALUE } & \text { REDUCED COST } \\\text { X1 } & .000000 & 4.000000 \\\text { X2 } & 8.000000 & .000000 \\\text { X3 } & .000000 & 4.000000\end{array}$$ $\begin{array}{rrr}\text { ROW } & \text { SLACK OR SURPLUS } & \text { DUAL PRICE }\\\text { 2) } & 4.000000 & .000000 \\3) & .000000 & -1.000000\end{array}$ NO. ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED: $$\begin{array} { c c c c } && { \text { OBJ. COEFFICIENT RANGES } } \\ & \text { CURRENT } & \text { ALLOWABLE } & \text { ALLOWABLE } \\\text { VARIABLE }&\text { COEFFICIENT }& \text { INCREASE } & \text { DECREASE } \\\hline \text { X1 } & 12.000000 & \text { INFINITY } & 4.000000 \\\text { X2 } & 10.000000 & 5.000000 & 10.000000 \\\text { X3 } & 9.000000 &\text { INFINITY } & 4.000000\\\end{array}$$ $\begin{array}{cccc}&&&\text { RIGHT HAND SIDE RANGES }\\&\text { CURRENT } & \text { ALLOWABLE }& \text { ALLOWABLE }\\\text { ROW } & \text { RHS } & \text { INCREASE } & \text { DECREASE } \\\hline2 & 60.000000 & 4.000000 & \text { INFINITY } \\3 & 80.000000 & \text { INFINITY } & 5.000000\end{array}$
a.What is the solution to the problem?
b.Which constraints are binding?
c.Interpret the reduced cost for x₁.
d.Interpret the dual price for constraint 2.
e.What would happen if the cost of x₁ dropped to 10 and the cost of x₂ increased to 12?