LINDO Output Is Given for the Following Linear Programming Problem $5 \mathrm { X } 1 + 8 \mathrm { X } 2 + 5 \mathrm { X } 3 > = 60$

question 1

Essay

LINDO output is given for the following linear programming problem.
MIN 12 X1 + 10 X2 + 9 X3
SUBJECT TO
END
LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1)80.000000
2) $5 \mathrm { X } 1 + 8 \mathrm { X } 2 + 5 \mathrm { X } 3 > = 60$
3) $8 X 1 + 10 X 2 + 5 X 3 > = 80$ $$\begin{array} { l r c } \text { VARIABLE } & \text { VALUE } & \text { REDUCED COST } \\\mathrm { X } 1 & .000000 & 4.000000 \\\mathrm { X } 2 & 8.000000 & .000000 \\\mathrm { X } 3 & .000000 & 4.000000\end{array}$$ NO.ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED:
$$\begin{array} { l c c } \text { ROW } & \text { SLACK OR SURPLUS } & \text { DUAL PRICE } \\\text { 2) } & 4.000000 & .000000 \\\text { 3) } & 000000 & - 1.000000\end{array}$$
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?

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