Solve the Following LP Problem Graphically Using Level Curves $\quad 8 \mathrm { X } _ { 1 } + 12 \mathrm { X } _ { 2 }$

question 30

Short Answer

Solve the following LP problem graphically using level curves.
MIN: $\quad 8 \mathrm { X } _ { 1 } + 12 \mathrm { X } _ { 2 }$
Subject to:
$$\begin{array} { l } 2 \mathrm { X } _ { 1 } + 1 \mathrm { X } _ { 2 } \geq 16 \\2 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } \geq 36 \\7 \mathrm { X } _ { 1 } + 8 \mathrm { X } _ { 2 } \geq 112 \\\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0\end{array}$$

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Definitions:

Depression

An economic depression is a prolonged period of significant decline in economic activity across a region or country, characterized by high unemployment, low consumer spending, and a decrease in industrial production.

National Output

The total value of all goods and services produced within a country's borders in a given time period.

Stagflation

A period of slow economic growth combined with high unemployment and rising prices (inflation).

Minor Recessions

Brief periods of economic decline during which trade and industrial activity are reduced, generally identified by a fall in GDP in successive quarters.