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.

Describe the conditions under which a security interest may apply, including prior to the debtor's possession of the collateral.

Recognize the significance and application of chattel paper in secured transactions.

Apply basic algebraic operations to simplify expressions.

Understand and apply the concept of like terms in algebraic expressions.

---

Definitions:

Replication

The process of duplicating or reproducing scientific research to verify its findings.

National Rate

A statistical measure that represents a specific activity or occurrence across an entire country, often expressed per unit of population.

Dependent Variables

In an experiment, these are the variables that are tested and measured to see if they are affected by changes in the independent variables.

Random Samples

A selection method that gives each member of a population an equal chance of being chosen, often used in research to ensure representativeness.