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?

---

Definitions:

Harvest Stage

The phase in a business or product lifecycle where maximum benefits and profits are extracted, often after the growth phase has plateaued.

Risk Averse

Refers to the preference of individuals or organizations to avoid risk, choosing the option with the least uncertainty.

Small Business Person

An individual who owns and operates a business that is typically defined by its small size in terms of revenue and number of employees.

Perseverance

The sustained effort and determination in spite of difficulties, obstacles, or discouragement, essential for achieving long-term goals.