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.

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Definitions:

Materials

Items or substances from which something is made or can be made, often used in the context of production or manufacturing.

FIFO Method

The First-In, First-Out (FIFO) method is an inventory valuation strategy where the oldest inventory items are recorded as sold first.

Equivalent Units

A concept used in process costing that converts partially completed units into a number of fully completed units, based on the percentage completion of those units.

Conversion

The process of changing raw materials into finished products or turning prospects into customers, depending on the context.