LINGO Output Is Given for the Following Linear Programming Problem

question 46

Essay

LINGO 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 $$\begin{array} { c c c } \text { VARIABLE } & \text { VALUE } & \text { REDUCED COST } \\\text { X1 } & .000000 & 4.000000 \\\text { X2 } & 8.000000 & .000000 \\\text { X3 } & .000000 & 4.000000\end{array}$$ $\begin{array}{l}\begin{array}{c}ROW&\text{SLACK OR SURPLUS}&\text{DUAL PRICE}\\\hline2)&4.000000 & .000000 \\3)&.000000 & -1.000000\end{array}\end{array}$ NO.ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED: $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { OBJ. COEFFICIENT RANGES }$
$\begin{array}{crrr}\underline{\text { VARIABLE }}&\frac{\text { CURRENT }}{\text { COEFFICIENT }} & \frac{\text { ALLOWABLE }}{\text { INCREASE }} & \frac{\text { ALLOWABLE }}{\text { DECREASE }}\\X 1 & 12.000000 & \text { INFINITY } & 4.000000 \\X 2 & 10.000000 & 5.000000 & 10.000000 \\X 3 & 9.000000 & \text { INFINITY } & 4.000000\end{array}$ $$\begin{array}{l}\begin{array} { c c c c } &&&\text { RIGHTHAND SIDE RANGES }\\& \text { CURRENT } & \text { ALLOWABLE } && \text { ALLOWABLE } \\\hline\text { ROW } & \text { RHS } & \text { INCREASE } && \text { DECREASE } \\2 & 60.000000 & 4.000000 && \text { INFINITY } \\3 & 80.000000 & \text { INFINITY } && 5.000000\end{array}\end{array}$$
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:

Floor Planning

A type of business loan generally made for “big-ticket” items. The business holds the item in inventory and pays interest, but it is actually owned by the lender until the item is sold.

Unsecured Loan

A loan that doesn't require collateral and is based on the borrower's creditworthiness.

Fixed-Rate Loan

A loan where the interest rate remains constant throughout the term of the loan, providing predictability in payments.

Mortgage Broker

A professional intermediary who facilitates the process of acquiring a mortgage loan for individuals or businesses.