Formulate this as LPP.
$begingroup$
A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.
linear-programming operations-research
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
$endgroup$
add a comment |
$begingroup$
A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.
linear-programming operations-research
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
$endgroup$
$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21
$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13
$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16
add a comment |
$begingroup$
A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.
linear-programming operations-research
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
$endgroup$
A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.
linear-programming operations-research
linear-programming operations-research
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
edited Jan 9 '17 at 7:46
projectilemotion
11.4k62141
11.4k62141
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
asked Jan 9 '17 at 7:21
Isha DhimanIsha Dhiman
245
245
$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21
$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13
$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16
add a comment |
$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21
$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13
$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16
$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21
$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21
$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13
$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13
$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16
$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$mathbf{text{Decision variable}}$
Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr
Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr
$mathbf{text{Subject to:}}$
$10 x_1 +5 x_2 ge 2000$
$x_1 le (50$ X $8) le 400$
$x_2 le (40$ X $8) le 320$
$x_1 ge 0$
$x_2 ge 0$
Minimise cost, $z$
$z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$
$z=44.25 x_1 + 12.375 x_2$
I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
$endgroup$
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%2f2089922%2fformulate-this-as-lpp%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
$begingroup$
$mathbf{text{Decision variable}}$
Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr
Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr
$mathbf{text{Subject to:}}$
$10 x_1 +5 x_2 ge 2000$
$x_1 le (50$ X $8) le 400$
$x_2 le (40$ X $8) le 320$
$x_1 ge 0$
$x_2 ge 0$
Minimise cost, $z$
$z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$
$z=44.25 x_1 + 12.375 x_2$
I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
$endgroup$
add a comment |
$begingroup$
$mathbf{text{Decision variable}}$
Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr
Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr
$mathbf{text{Subject to:}}$
$10 x_1 +5 x_2 ge 2000$
$x_1 le (50$ X $8) le 400$
$x_2 le (40$ X $8) le 320$
$x_1 ge 0$
$x_2 ge 0$
Minimise cost, $z$
$z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$
$z=44.25 x_1 + 12.375 x_2$
I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
$endgroup$
add a comment |
$begingroup$
$mathbf{text{Decision variable}}$
Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr
Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr
$mathbf{text{Subject to:}}$
$10 x_1 +5 x_2 ge 2000$
$x_1 le (50$ X $8) le 400$
$x_2 le (40$ X $8) le 320$
$x_1 ge 0$
$x_2 ge 0$
Minimise cost, $z$
$z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$
$z=44.25 x_1 + 12.375 x_2$
I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
$endgroup$
$mathbf{text{Decision variable}}$
Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr
Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr
$mathbf{text{Subject to:}}$
$10 x_1 +5 x_2 ge 2000$
$x_1 le (50$ X $8) le 400$
$x_2 le (40$ X $8) le 320$
$x_1 ge 0$
$x_2 ge 0$
Minimise cost, $z$
$z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$
$z=44.25 x_1 + 12.375 x_2$
I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
answered Jan 21 '17 at 8:03
Tos HinaTos Hina
1,037619
1,037619
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.
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%2f2089922%2fformulate-this-as-lpp%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
$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21
$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13
$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16