Given the Following Linear Programming Problem
Max Z
0 $\le$ 24
1x₁ + 1

question 24

Essay

Given the following linear programming problem
Max Z
0.5x₁ + 6x₂ + 5x₃
s.t.
4x₁ + 6x₂ + 3x₃ $\le$ 24
1x₁ + 1.5x₂ + 3x₃ $\le$ 12
3x₁ + x₂ $\le$ 12
and the final tableau is $$\begin{array} { c c | c c c c c c | c } & & \mathrm { x } _ { 1 } & \mathrm { x } _ { 2 } & \mathrm { x } _ { 3 } & \mathrm {~s} _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } & \\\text { Basis } & \mathrm { c } _ { \mathrm { B } } & .5 & 6 & 5 & 0 & 0 & 0 & \\\hline \mathrm { x } _ { 2 } & 6 & 1 & 1 & 0 & .22 & - .22 & 0 & 2.67 \\\mathrm { x } _ { 3 } & 5 & 0 & 0 & 1 & .11 & - .44 & 0 & 2.67 \\\mathrm {~s} _ { 3 } & 0 & 2.33 & 0 & 0 & - .22 & .22 & 1 & 9.33 \\\hline & \mathrm { z } _ { \mathrm { j } } & 4 & 6 & 5 & .77 & .88 & 0 & 29.33 \\& \mathrm { c } _ { \mathrm { j } } - \mathrm { z } _ { \mathrm { j } } & .5 & 0 & 0 & - .77 & - .88 & 0 &\end{array}$$
a.Find the range of optimality for c_1, c_2, c_3, c_4, c_5, and c₆.
b.Find the range of feasibility for b₁, b₂, and b₃.

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Definitions:

Formal Operational Period

In Piaget’s theory, the period from about age twelve on, in which a child can think abstractly and consider hypothetical possibilities.

Abstract Reasoning Skills

These skills involve the ability to analyze information, detect patterns and relationships, and solve problems on a complex, abstract level.

Formal Operational Period

A stage of cognitive development proposed by Piaget, where individuals (around 12 years and older) start to think abstractly, reason logically, and use deductive reasoning.

Sensorimotor

Relating to or involving both sensory and motor functions or pathways.