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:

Cash Concentration Account

A bank account used by companies to consolidate and manage cash from multiple locations or accounts, improving liquidity management.

Collection Float

The time delay between when a check is written and when it is actually deducted from the payer's account, impacting the receiver's cash flow.

Disbursement Float

The time delay between when a check is issued and when the funds are actually withdrawn from the payer's account.

Ledger Balance

The total amount recorded in a company's ledger, representing the total assets, liabilities, and shareholders' equity at a specific time.