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:

Operational Sex Ratio

The ratio of sexually active males to receptive females in a population at any given time, affecting mating behavior and strategy.

Two-Fold Cost of Sex

A hypothesis in evolutionary biology that suggests sexual reproduction is twice as costly as asexual reproduction, since only females contribute to the gene pool of the offspring.

Sexual Lineages

The genetic line of descent traced through mating and reproduction, typically examined through the analysis of patterns in genetic variation.

Asexual Lineages

Populations or species that reproduce without the genetic recombination processes involved in sexual reproduction.