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Assignment in book:

Farmer Jones must determine how many acres of corn and wheat to plant this year. An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week. An acre of corn yields 10 bushels of corn and requires 4 hours of labor per week. All wheat can be sold at \$4 a bushel, and all corn can be sold at \$3 a bushel. Seven acres of land and 40 hours per week of labor are available. Government regulations require that at least 30 bushels of corn be produced during the current year. Let $x_1$ = number of acres of corn planted, and $x_2$ = number of acres of wheat planted. Using these decision variables, formulate an LP whose solution will tell Farmer Jones how to maximize the total revenue from wheat and corn.

I struggle to understand why the Government constraint should be: $x_1 \geq 3$.

Can someone explain it to me step by step?

Thanks!

Daniel Cunha
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Hikato
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  • It is not the translation of the sentences "Government regulations require that at least 30 bushels of corn be produced during the current year." and "An acre of corn yields 10 bushels of corn." ? Otherwise, you may find an answer faster on economics.SE... – Evargalo Sep 29 '17 at 11:44
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    Since you are new here, and since you asked several questions without accepting an answer: After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark ✓ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?. You should go through your old questions. – P. Siehr Sep 29 '17 at 11:49

2 Answers2

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Hint: These are the important parts of the text, which are sufficient to answer your question.

  • $x_1$ is the number of acres of corn.

  • One acre yields 10 bushels of corn.

  • The government requires 30 bushels of corn.

Can you take it from here?

P. Siehr
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If I've got it right, we want to maximize the profit function $h(x_1,x_2)$

$h(x_1,x_2) = (3 \cdot 10)\,x_1 + (4 \cdot 25)\,x_2$

Subjected to the constraints:

$x_1 + x_2 = 7$ (acres)

$4\,x_1 + 10\,x_2 \leq 40$ (hours per week of labor)

$x_1 \geq 3$ (government regulation)

Can we use fractions of an acre? Or $x_1,x_2\in\mathbb{N}$?

Daniel Cunha
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