How do I convert this into a linear programming problem?
A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50 and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and tiller, are rented. The tractor is available for 200 hours, and the tiller is available for 100 hours, Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. How many acres of each crop should be planted to maximize the farmer's profit?
I'll try to use simplex method, afterwards.
linear-algebra linear-programming
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
asked Mar 29 '15 at 22:48
randevrandev
63
add a comment |
A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50 and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and tiller, are rented. The tractor is available for 200 hours, and the tiller is available for 100 hours, Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. How many acres of each crop should be planted to maximize the farmer's profit?
I'll try to use simplex method, afterwards.
linear-algebra linear-programming
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
asked Mar 29 '15 at 22:48
randevrandev
63
add a comment |
A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50 and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and tiller, are rented. The tractor is available for 200 hours, and the tiller is available for 100 hours, Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. How many acres of each crop should be planted to maximize the farmer's profit?
I'll try to use simplex method, afterwards.
linear-algebra linear-programming
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
asked Mar 29 '15 at 22:48
randevrandev
63
A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50 and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and tiller, are rented. The tractor is available for 200 hours, and the tiller is available for 100 hours, Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. How many acres of each crop should be planted to maximize the farmer's profit?
I'll try to use simplex method, afterwards.
linear-algebra linear-programming
linear-algebra linear-programming
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
asked Mar 29 '15 at 22:48
randevrandev
63
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
asked Mar 29 '15 at 22:48
randevrandev
63
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
edited Mar 29 '15 at 22:51
George V. Williams
4,50321746
4,50321746
asked Mar 29 '15 at 22:48
randevrandev
63
asked Mar 29 '15 at 22:48
randevrandev
63
asked Mar 29 '15 at 22:48
randevrandev
63
63
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
The first step is to describe what your variables are: $x$ which could be the number of acres of Barley sown, and $y$ which could be the number of acres of wheat.
Now, what is the profit function: $P = 70x + 50y$ (70 dollars per acre of barley + 50 dollars per acre of wheat).
Now, what are the constraints: certainly $xgeq 0$ and $ygeq 0$. What about not overusing the tiller?
$$2x + 1y leq 100$$ 2 hours on tiller for each acre of barley, 1 hour for each acre of wheat... not more than 100 hours available.
Similarly, what about not overusing the tractor?
$$3x + 4y leq 200$$ 3 hours on tractor for each acre of barley, 4 hours on the tractor for each acre of wheat... not more than 200 hours total on the tractor.
Condensing all those constraints you have:
Maximize $P=70x + 50y$
Subject to
begin{align*}
2x + 1y &leq 100 \
3x + 4y &leq 200 \
x, y &geq 0
end{align*}
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1212117%2fhow-do-i-convert-this-into-a-linear-programming-problem%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
The first step is to describe what your variables are: $x$ which could be the number of acres of Barley sown, and $y$ which could be the number of acres of wheat.
Now, what is the profit function: $P = 70x + 50y$ (70 dollars per acre of barley + 50 dollars per acre of wheat).
Now, what are the constraints: certainly $xgeq 0$ and $ygeq 0$. What about not overusing the tiller?
$$2x + 1y leq 100$$ 2 hours on tiller for each acre of barley, 1 hour for each acre of wheat... not more than 100 hours available.
Similarly, what about not overusing the tractor?
$$3x + 4y leq 200$$ 3 hours on tractor for each acre of barley, 4 hours on the tractor for each acre of wheat... not more than 200 hours total on the tractor.
Condensing all those constraints you have:
Maximize $P=70x + 50y$
Subject to
begin{align*}
2x + 1y &leq 100 \
3x + 4y &leq 200 \
x, y &geq 0
end{align*}
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
add a comment |
The first step is to describe what your variables are: $x$ which could be the number of acres of Barley sown, and $y$ which could be the number of acres of wheat.
Now, what is the profit function: $P = 70x + 50y$ (70 dollars per acre of barley + 50 dollars per acre of wheat).
Now, what are the constraints: certainly $xgeq 0$ and $ygeq 0$. What about not overusing the tiller?
$$2x + 1y leq 100$$ 2 hours on tiller for each acre of barley, 1 hour for each acre of wheat... not more than 100 hours available.
Similarly, what about not overusing the tractor?
$$3x + 4y leq 200$$ 3 hours on tractor for each acre of barley, 4 hours on the tractor for each acre of wheat... not more than 200 hours total on the tractor.
Condensing all those constraints you have:
Maximize $P=70x + 50y$
Subject to
begin{align*}
2x + 1y &leq 100 \
3x + 4y &leq 200 \
x, y &geq 0
end{align*}
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
add a comment |
The first step is to describe what your variables are: $x$ which could be the number of acres of Barley sown, and $y$ which could be the number of acres of wheat.
Now, what is the profit function: $P = 70x + 50y$ (70 dollars per acre of barley + 50 dollars per acre of wheat).
Now, what are the constraints: certainly $xgeq 0$ and $ygeq 0$. What about not overusing the tiller?
$$2x + 1y leq 100$$ 2 hours on tiller for each acre of barley, 1 hour for each acre of wheat... not more than 100 hours available.
Similarly, what about not overusing the tractor?
$$3x + 4y leq 200$$ 3 hours on tractor for each acre of barley, 4 hours on the tractor for each acre of wheat... not more than 200 hours total on the tractor.
Condensing all those constraints you have:
Maximize $P=70x + 50y$
Subject to
begin{align*}
2x + 1y &leq 100 \
3x + 4y &leq 200 \
x, y &geq 0
end{align*}
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
The first step is to describe what your variables are: $x$ which could be the number of acres of Barley sown, and $y$ which could be the number of acres of wheat.
Now, what is the profit function: $P = 70x + 50y$ (70 dollars per acre of barley + 50 dollars per acre of wheat).
Now, what are the constraints: certainly $xgeq 0$ and $ygeq 0$. What about not overusing the tiller?
$$2x + 1y leq 100$$ 2 hours on tiller for each acre of barley, 1 hour for each acre of wheat... not more than 100 hours available.
Similarly, what about not overusing the tractor?
$$3x + 4y leq 200$$ 3 hours on tractor for each acre of barley, 4 hours on the tractor for each acre of wheat... not more than 200 hours total on the tractor.
Condensing all those constraints you have:
Maximize $P=70x + 50y$
Subject to
begin{align*}
2x + 1y &leq 100 \
3x + 4y &leq 200 \
x, y &geq 0
end{align*}
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
answered Mar 29 '15 at 22:58
TravisJTravisJ
6,35831730
6,35831730
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1212117%2fhow-do-i-convert-this-into-a-linear-programming-problem%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
