Given the Following Linear Programming Problem
Max
10x₁ + 12x₂ $\ge$

question 4

Essay

Given the following linear programming problem
Max
10x₁ + 12x₂
s.t.
1x₁ + 2x₂ $\ge$ 40
5x₁ + 8x₂ $\le$ 160
1x₁ + 1x₂ $\le$ 40
x₁, x₂ $\ge$ 0
the final tableau is $$\begin{array} { c c | c c c c c | c } & & \mathrm { x } _ { 1 } & \mathrm { x } _ { 2 } & \mathrm {~s} _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } & \\\text { Basis } & \mathrm { c } _ { \mathrm { B } } & 10 & 12 & 0 & 0 & 0 & \\\hline \mathrm { x } _ { 2 } & 12 & 0 & 1 & - 2.5 & - .5 & 0 & 20 \\\mathrm { x } _ { 1 } & 10 & 1 & 0 & 4 & 1 & 0 & 0 \\\mathrm {~s} _ { 3 } & 0 & 0 & 0 & - 1.5 & - 5 & 1 & 20 \\\hline & \mathrm { z } _ { \mathrm { j } } & 10 & 12 & 10 & 4 & 0 & 240 \\& \mathrm { c } _ { \mathrm { j } } - \mathrm { z } _ { \mathrm { j } } & 0 & 0 & - 10 & - 4 & 0 &\end{array}$$
a.Find the range of optimality for c₁ and c₂.
b.Find the range of feasibility for b₁, b₂, and b₃.
c.Find the dual prices.

Acknowledge the role of international figures and conflicts in shaping early American foreign policy and domestic politics.

Recognize the founding fathers' stance on political parties and their vision for America's political system.

Identify the main sources of political divisions in the early republic, particularly regarding financial and economic plans.

Analyze the reasons behind opposition to Alexander Hamilton's economic plan by figures such as Thomas Jefferson and James Madison.

---

Definitions:

Memories

The mental faculty for recalling or recognizing previous experiences or information.

Behavior Patterns

Behavior patterns refer to recurrent ways of acting or responding that are characteristic of an individual or group.

Dominant Source

The primary or most influential source of information or authority in a given context.

Sensual Pleasure

Gratification obtained through engaging the senses, often emphasizing the importance of tactile, olfactory, gustatory, auditory, and visual experiences.