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?

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Definitions:

Mediators

Neutral individuals or parties that facilitate negotiation and conflict resolution between disputing parties without making a binding decision.

Communication Process

The method by which information is transferred from one person or group to another, encompassing several elements including sender, message, medium, receiver, and feedback.

Specialized Form

Specialized form refers to a distinct variation or adaptation of something that is designed for a specific purpose or function.

Binding Arbitration

A legal process in which a dispute is resolved by an arbitrator, with the decision being final and enforceable by law.