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20 Practice Tests Question of the Day Flashcards Learn by Concept

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Flashcards: Linear Programming

A farm has 750 acres of land available for planting crops. The possible crops are soy, corn, and oats. There is 1,200 acre-ft of water for irrigation and the crew will be able to work of the farm 575 hours per week.

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&2.2&1.1&1.2\\ Labor & 0.9&0.1&0.2\\ Money Made&400&250&300 \\ \hline\end{tabular}$

$\\x_1=500 \\x_2=65 \\x_3=15\\y=\$233,500$

$\\x_1=65 \\x_2=0 \\x_3=510\\y=\$223,500$

$\\x_1=150 \\x_2=70 \\x_3=65\\y=\$243,500$

$\\x_1=510 \\x_2=0 \\x_3=65\\y=\$223,500$

$\\x_1=210 \\x_2=100 \\x_3=65\\y=\$253,300$

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Flashcards: Linear Programming

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&2.2&1.1&1.2\\ Labor & 0.9&0.1&0.2\\ Money Made&400&250&300 \\ \hline\end{tabular}$

Your answer:

$\\x_1=500 \\x_2=65 \\x_3=15\\y=\$233,500$

Your answer:

$\\x_1=65 \\x_2=0 \\x_3=510\\y=\$223,500$

Your answer:

$\\x_1=150 \\x_2=70 \\x_3=65\\y=\$243,500$

Your answer:

$\\x_1=210 \\x_2=100 \\x_3=65\\y=\$253,300$

Correct answer:

$\\x_1=510 \\x_2=0 \\x_3=65\\y=\$223,500$

Explanation:

The objective of this particular problem is to maximize the profit.

Maximize the function:

y=f(x_1,...,x_n)=c_1x_1+...+c_nx_n

over the region defined by the constraints.

First identify the variables and assumptions of the problem.

$\\x_1=\text{acres of soy planted} \\x_2=\text{acres of corn planted} \\x_3=\text{acres of oats planted} \\l=\text{labor required} \\w=\text{water required} \\t=\text{total acreage planted} \\y=\text{total profit}$

$\\w=2.2x_1+1.1x_2+1.2x_3 \\l=0.9x_1+0.1x_2+0.2x_3 \\t=x_1+x_2+x_3 \\y=400x_1+250x_2+300x_3 \\w\leq 1200 \\l\leq 750 \\t\leq 575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

Now using the constraints formulate the linear programming model.

$\\2.2x_1+1.1x_2+1.2x_3\leq1200 \\0.9x_1+0.1x_2+0.2x_3\leq750 \\x_1+x_2+x_3\leq575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

From here use computer implementation to solve using the simplex method.

$\\x_1=510 \\x_2=0 \\x_3=65$

Therefore, the optimal solution will occur when there are 510 acres of soy planted and 65 acres of oats.

The maximum profit at this solution will be, $223,500.

Flashcards: Linear Programming

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&1.2&3.4&1.9\\ Labor & 0.1&0.8&0.3\\ Money Made&300&550&200 \\ \hline\end{tabular}$

$\\x_1=231.818 \\x_2=0 \\x_3=343.182\\y=\$230,454.50$

$\\x_1=0 \\x_2=231.818 \\x_3=343.182\\y=\$230,454.50$

$\\x_1=231.818 \\x_2= 343.182 \\x_3=0\\y=\$230,454.50$

$\\x_1=343.182 \\x_2=0 \\x_3= 231.818\\y=\$230,454.50$

$\\x_1=343.182 \\x_2=231.818 \\x_3=0\\y=\$230,454.50$

Report an Error Copyright Notice

Flashcards: Linear Programming

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&1.2&3.4&1.9\\ Labor & 0.1&0.8&0.3\\ Money Made&300&550&200 \\ \hline\end{tabular}$

Your answer:

$\\x_1=231.818 \\x_2=0 \\x_3=343.182\\y=\$230,454.50$

Your answer:

$\\x_1=0 \\x_2=231.818 \\x_3=343.182\\y=\$230,454.50$

Your answer:

$\\x_1=231.818 \\x_2= 343.182 \\x_3=0\\y=\$230,454.50$

Your answer:

$\\x_1=343.182 \\x_2=0 \\x_3= 231.818\\y=\$230,454.50$

Correct answer:

$\\x_1=343.182 \\x_2=231.818 \\x_3=0\\y=\$230,454.50$

Explanation:

The objective of this particular problem is to maximize the profit.

Maximize the function:

y=f(x_1,...,x_n)=c_1x_1+...+c_nx_n

over the region defined by the constraints.

First identify the variables and assumptions of the problem.

$\\w=1.2x_1+3.4x_2+1.9x_3 \\l=0.1x_1+0.8x_2+0.3x_3 \\t=x_1+x_2+x_3 \\y=300x_1+550x_2+200x_3 \\w\leq 1200 \\l\leq 750 \\t\leq 575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

Now using the constraints formulate the linear programming model.

$\\1.2x_1+3.4x_2+1.9x_3\leq1200 \\0.1x_1+0.8x_2+0.3x_3\leq750 \\x_1+x_2+x_3\leq575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

From here use computer implementation to solve using the simplex method.

$\\x_1=343.182 \\x_2=231.818 \\x_3=0$

Therefore, the optimal solution will occur when there are 343.182 acres of soy planted and 231.818 acres of corn planted.

The maximum profit at this solution will be, $230,454.50.

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Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

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DMCA Complaint

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K-8

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All Math Modeling Resources

Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

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