Solve the Following LP Problem Graphically Using Level Curves $\quad 5 \mathrm { X } _ { 1 } + 7 \mathrm { X } _ { 2 }$

question 3

Short Answer

Solve the following LP problem graphically using level curves.
MiN: $\quad 5 \mathrm { X } _ { 1 } + 7 \mathrm { X } _ { 2 }$
Subject to: $\quad 4 X _ { 1 } + 1 X _ { 2 } \geq 16$
$6 \mathrm { X } _ { 1 } + 5 \mathrm { X } _ { 2 } \geq 60$
$5 \mathrm { X } _ { 1 } + 8 \mathrm { X } _ { 2 } \geq 80$
$\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0$

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Definitions:

Food Production

The process of cultivating plants and raising livestock for the purpose of providing food for consumption.

Per Capita Incomes

The average income earned per person in a certain area in a specified year.

Agricultural Products

Goods derived from agriculture and farming activities, including crops, livestock, and other raw materials.

Farm Households

Families living and working on farms, often combining both their living quarters and business operations in the same place.