Eight of the Entries Have Been Deleted from the LINGO

question 23

Essay

Eight of the entries have been deleted from the LINGO output that follows.Use what you know about linear programming to find values for the blanks.
MIN 6 X1 + 7.5 X2 + 10 X3
SUBJECT TO
2)25 X1 + 35 X2 + 30 X3 >= 2400
3)2 X1 + 4 X2 + 8 X3 >= 400
END
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1)612.50000 $$\begin{array} { c c c } \text { VARIABLE } & \text { VALUE } & \text { REDUCED COST } \\\text { X1 } & - & 1.312500 \\\text { X2 } & - & -\\\text { X3 } &27.500000 &- \\\hline\end{array}$$ $$\begin{array} { c c c } ROW& \text { SLACK OR SURPLUS } & \text { DUAL PRICE } \\\hline2)&-&-.125000 \\3)&-&-.781250\end{array}$$ NO.ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED: $$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { OBJ. COEFFICIENT RANGES }\\\begin{array} { c c c c c } \text { VARIABLE } & \frac { \text { CURRENT } } { \text { COEFFICIENT } } & \frac { \text { ALLOWAB LE } } { \text { INCREASE } } & & \frac { \text { ALLWABLE } } { \text { DECREASE } } \\\text { X1 } & 6.000000 & -&&- \\\text { X2 } & 7.500000 & 1.500000 & & 2.500000 \\\text { X3 } & 10.000000 & 5.000000 && 3.571429\end{array}\end{array}$$ $\begin{array}{cccc}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { RIGHTHAND SIDE RANGES }\\\begin{array}{cccc}&\text { CURRENT } & \text { ALLOWABLE } & \text { ALLOWABLE } \\\hline\mathrm{ROW}& \text { RHS } & \text { INCREASE } & \text { DECREASE } \\2&2400.000000 & 1100.000000 & 900.000000 \\3&400.000000 & 240.000000 & 125.714300\end{array}\end{array}$

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Definitions:

A Priori Method

A method of reasoning based on theoretical deduction rather than empirical evidence.

Critical Theory

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