How many kilograms of each type of fertilizer should the farmer use?Linear Programming optimization with multiple optimal solutionsBerlin Airlift Linear Optimization ProblemApplication of queueing theoryoptimizing contractor schedules - operations research linear programmingProblem in forming linear equations in Linear Programming problemCheese producerA farmer wishes to employ apple pickers during harvest timeWhat is the objective function and constraints of this problem?Just need a clarification on the optimization problemLinear Programming Inventory Levels / Hiring and Firing WorkersCriteria in Capacitated Vehicle Routing Problem
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How many kilograms of each type of fertilizer should the farmer use?
Linear Programming optimization with multiple optimal solutionsBerlin Airlift Linear Optimization ProblemApplication of queueing theoryoptimizing contractor schedules - operations research linear programmingProblem in forming linear equations in Linear Programming problemCheese producerA farmer wishes to employ apple pickers during harvest timeWhat is the objective function and constraints of this problem?Just need a clarification on the optimization problemLinear Programming Inventory Levels / Hiring and Firing WorkersCriteria in Capacitated Vehicle Routing Problem
$begingroup$
A farmer has a supply of chemical fertilizer of type A which contains 10% nitrogen and 5% phosphoric acid, and type B which contains 6% nitrogen and 10% phosphoric acid. After testing the soil conditions of the field, it was found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for producing a good crop. The fertilizer of type A costs Rs.5 per kg and the type B costs Rs.3 per kg. How many kg of each type of the fertilizer should be used to meet the requirement at the minimum possible cost? Using L.P.P. solve the above problem graphically.
linear-programming operations-research
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 10:01
user74981user74981
163
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
|
show 1 more comment
$begingroup$
A farmer has a supply of chemical fertilizer of type A which contains 10% nitrogen and 5% phosphoric acid, and type B which contains 6% nitrogen and 10% phosphoric acid. After testing the soil conditions of the field, it was found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for producing a good crop. The fertilizer of type A costs Rs.5 per kg and the type B costs Rs.3 per kg. How many kg of each type of the fertilizer should be used to meet the requirement at the minimum possible cost? Using L.P.P. solve the above problem graphically.
linear-programming operations-research
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 10:01
user74981user74981
163
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Aside from typing the raw text of your homework, what effort have you made ? Unless you say where you are blocked, this question will be closed...
$endgroup$
– Jean Marie
Mar 13 at 12:10
$begingroup$
@JeanMarie hey there I have tried this and actually wanted to attach it with the question but as I am new here and lack experience with this platform I am not able to, it says I need 10 notices or something to be able to post them my equations are 10x+6y greater than or = 1400 and 5x+10y greater than or = 1400
$endgroup$
– user74981
Mar 13 at 12:13
$begingroup$
@JeanMarie I am almost at the answer if there's any way I could post the picture so you guys could review it do let me know
$endgroup$
– user74981
Mar 13 at 12:16
$begingroup$
Very well. Each one of these inequalities (to which you should add $x geq 0$ and $y geq 0$) defines a half-plane : hatch each of them ; the quadrilateral region which is hatched four times is the "feasible region". Now take a moving line $ax+by=m$... that should be just touching the feasible region, as you have been taught, I assume in your lectures.
$endgroup$
– Jean Marie
Mar 13 at 12:19
$begingroup$
@JeanMarie I got Zmin min at two points (80,100) and (0, 700/3) the value of Zmin in both cases is 700 now how do we chose between them ? When both the points have same value
$endgroup$
– user74981
Mar 13 at 12:23
|
show 1 more comment
$begingroup$
A farmer has a supply of chemical fertilizer of type A which contains 10% nitrogen and 5% phosphoric acid, and type B which contains 6% nitrogen and 10% phosphoric acid. After testing the soil conditions of the field, it was found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for producing a good crop. The fertilizer of type A costs Rs.5 per kg and the type B costs Rs.3 per kg. How many kg of each type of the fertilizer should be used to meet the requirement at the minimum possible cost? Using L.P.P. solve the above problem graphically.
linear-programming operations-research
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 10:01
user74981user74981
163
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
A farmer has a supply of chemical fertilizer of type A which contains 10% nitrogen and 5% phosphoric acid, and type B which contains 6% nitrogen and 10% phosphoric acid. After testing the soil conditions of the field, it was found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for producing a good crop. The fertilizer of type A costs Rs.5 per kg and the type B costs Rs.3 per kg. How many kg of each type of the fertilizer should be used to meet the requirement at the minimum possible cost? Using L.P.P. solve the above problem graphically.
linear-programming operations-research
linear-programming operations-research
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 10:01
user74981user74981
163
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 10:01
user74981user74981
163
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
edited Mar 13 at 12:28
Rodrigo de Azevedo
13.1k41960
13.1k41960
asked Mar 13 at 10:01
user74981user74981
163
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 10:01
user74981user74981
163
asked Mar 13 at 10:01
user74981user74981
163
163
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user74981 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Aside from typing the raw text of your homework, what effort have you made ? Unless you say where you are blocked, this question will be closed...
$endgroup$
– Jean Marie
Mar 13 at 12:10
$begingroup$
@JeanMarie hey there I have tried this and actually wanted to attach it with the question but as I am new here and lack experience with this platform I am not able to, it says I need 10 notices or something to be able to post them my equations are 10x+6y greater than or = 1400 and 5x+10y greater than or = 1400
$endgroup$
– user74981
Mar 13 at 12:13
$begingroup$
@JeanMarie I am almost at the answer if there's any way I could post the picture so you guys could review it do let me know
$endgroup$
– user74981
Mar 13 at 12:16
$begingroup$
Very well. Each one of these inequalities (to which you should add $x geq 0$ and $y geq 0$) defines a half-plane : hatch each of them ; the quadrilateral region which is hatched four times is the "feasible region". Now take a moving line $ax+by=m$... that should be just touching the feasible region, as you have been taught, I assume in your lectures.
$endgroup$
– Jean Marie
Mar 13 at 12:19
$begingroup$
@JeanMarie I got Zmin min at two points (80,100) and (0, 700/3) the value of Zmin in both cases is 700 now how do we chose between them ? When both the points have same value
$endgroup$
– user74981
Mar 13 at 12:23
|
show 1 more comment
1
$begingroup$
Aside from typing the raw text of your homework, what effort have you made ? Unless you say where you are blocked, this question will be closed...
$endgroup$
– Jean Marie
Mar 13 at 12:10
$begingroup$
@JeanMarie hey there I have tried this and actually wanted to attach it with the question but as I am new here and lack experience with this platform I am not able to, it says I need 10 notices or something to be able to post them my equations are 10x+6y greater than or = 1400 and 5x+10y greater than or = 1400
$endgroup$
– user74981
Mar 13 at 12:13
$begingroup$
@JeanMarie I am almost at the answer if there's any way I could post the picture so you guys could review it do let me know
$endgroup$
– user74981
Mar 13 at 12:16
$begingroup$
Very well. Each one of these inequalities (to which you should add $x geq 0$ and $y geq 0$) defines a half-plane : hatch each of them ; the quadrilateral region which is hatched four times is the "feasible region". Now take a moving line $ax+by=m$... that should be just touching the feasible region, as you have been taught, I assume in your lectures.
$endgroup$
– Jean Marie
Mar 13 at 12:19
$begingroup$
@JeanMarie I got Zmin min at two points (80,100) and (0, 700/3) the value of Zmin in both cases is 700 now how do we chose between them ? When both the points have same value
$endgroup$
– user74981
Mar 13 at 12:23
1
1
$begingroup$
Aside from typing the raw text of your homework, what effort have you made ? Unless you say where you are blocked, this question will be closed...
$endgroup$
– Jean Marie
Mar 13 at 12:10
$begingroup$
Aside from typing the raw text of your homework, what effort have you made ? Unless you say where you are blocked, this question will be closed...
$endgroup$
– Jean Marie
Mar 13 at 12:10
$begingroup$
@JeanMarie hey there I have tried this and actually wanted to attach it with the question but as I am new here and lack experience with this platform I am not able to, it says I need 10 notices or something to be able to post them my equations are 10x+6y greater than or = 1400 and 5x+10y greater than or = 1400
$endgroup$
– user74981
Mar 13 at 12:13
$begingroup$
@JeanMarie hey there I have tried this and actually wanted to attach it with the question but as I am new here and lack experience with this platform I am not able to, it says I need 10 notices or something to be able to post them my equations are 10x+6y greater than or = 1400 and 5x+10y greater than or = 1400
$endgroup$
– user74981
Mar 13 at 12:13
$begingroup$
@JeanMarie I am almost at the answer if there's any way I could post the picture so you guys could review it do let me know
$endgroup$
– user74981
Mar 13 at 12:16
$begingroup$
@JeanMarie I am almost at the answer if there's any way I could post the picture so you guys could review it do let me know
$endgroup$
– user74981
Mar 13 at 12:16
$begingroup$
Very well. Each one of these inequalities (to which you should add $x geq 0$ and $y geq 0$) defines a half-plane : hatch each of them ; the quadrilateral region which is hatched four times is the "feasible region". Now take a moving line $ax+by=m$... that should be just touching the feasible region, as you have been taught, I assume in your lectures.
$endgroup$
– Jean Marie
Mar 13 at 12:19
$begingroup$
Very well. Each one of these inequalities (to which you should add $x geq 0$ and $y geq 0$) defines a half-plane : hatch each of them ; the quadrilateral region which is hatched four times is the "feasible region". Now take a moving line $ax+by=m$... that should be just touching the feasible region, as you have been taught, I assume in your lectures.
$endgroup$
– Jean Marie
Mar 13 at 12:19
$begingroup$
@JeanMarie I got Zmin min at two points (80,100) and (0, 700/3) the value of Zmin in both cases is 700 now how do we chose between them ? When both the points have same value
$endgroup$
– user74981
Mar 13 at 12:23
$begingroup$
@JeanMarie I got Zmin min at two points (80,100) and (0, 700/3) the value of Zmin in both cases is 700 now how do we chose between them ? When both the points have same value
$endgroup$
– user74981
Mar 13 at 12:23
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
Your inequalities are right. Now see here how to solve the a linear program graphically. Below the picture shows the graph of your problem.
I got $Z_min$ min at two points (80,100) and (0, 700/3) the value of Zmin
in both cases is 700 now how do we chose between them ?
As you see at the graph that after the shift the objective function lies direcly on the first constraint $ygeq frac7003-frac53cdot x$. If we solve the objective function for y we get $y=fracz3-frac53cdot x$
The reason why the objective function lies directly on the first constraint is that both have the same slope of $-frac53$.
Thus the optimal solution is on every point on the constraint.
$(x^*,y^*)=left(x, frac7003-frac53cdot xright)$, where $0leq xleq 80$
So both solutions you mentioned are valid. But all solutions in between them as well.
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
$endgroup$
$begingroup$
Thank you very much! Really appreciated, I learnt something new today
$endgroup$
– user74981
Mar 13 at 13:51
$begingroup$
@user74981 You are welcome. I´m glad that it helps.
$endgroup$
– callculus
Mar 13 at 13:53
add a comment |
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1 Answer
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$begingroup$
Your inequalities are right. Now see here how to solve the a linear program graphically. Below the picture shows the graph of your problem.
I got $Z_min$ min at two points (80,100) and (0, 700/3) the value of Zmin
in both cases is 700 now how do we chose between them ?
As you see at the graph that after the shift the objective function lies direcly on the first constraint $ygeq frac7003-frac53cdot x$. If we solve the objective function for y we get $y=fracz3-frac53cdot x$
The reason why the objective function lies directly on the first constraint is that both have the same slope of $-frac53$.
Thus the optimal solution is on every point on the constraint.
$(x^*,y^*)=left(x, frac7003-frac53cdot xright)$, where $0leq xleq 80$
So both solutions you mentioned are valid. But all solutions in between them as well.
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
$endgroup$
$begingroup$
Thank you very much! Really appreciated, I learnt something new today
$endgroup$
– user74981
Mar 13 at 13:51
$begingroup$
@user74981 You are welcome. I´m glad that it helps.
$endgroup$
– callculus
Mar 13 at 13:53
add a comment |
$begingroup$
Your inequalities are right. Now see here how to solve the a linear program graphically. Below the picture shows the graph of your problem.
I got $Z_min$ min at two points (80,100) and (0, 700/3) the value of Zmin
in both cases is 700 now how do we chose between them ?
As you see at the graph that after the shift the objective function lies direcly on the first constraint $ygeq frac7003-frac53cdot x$. If we solve the objective function for y we get $y=fracz3-frac53cdot x$
The reason why the objective function lies directly on the first constraint is that both have the same slope of $-frac53$.
Thus the optimal solution is on every point on the constraint.
$(x^*,y^*)=left(x, frac7003-frac53cdot xright)$, where $0leq xleq 80$
So both solutions you mentioned are valid. But all solutions in between them as well.
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
$endgroup$
$begingroup$
Thank you very much! Really appreciated, I learnt something new today
$endgroup$
– user74981
Mar 13 at 13:51
$begingroup$
@user74981 You are welcome. I´m glad that it helps.
$endgroup$
– callculus
Mar 13 at 13:53
add a comment |
$begingroup$
Your inequalities are right. Now see here how to solve the a linear program graphically. Below the picture shows the graph of your problem.
I got $Z_min$ min at two points (80,100) and (0, 700/3) the value of Zmin
in both cases is 700 now how do we chose between them ?
As you see at the graph that after the shift the objective function lies direcly on the first constraint $ygeq frac7003-frac53cdot x$. If we solve the objective function for y we get $y=fracz3-frac53cdot x$
The reason why the objective function lies directly on the first constraint is that both have the same slope of $-frac53$.
Thus the optimal solution is on every point on the constraint.
$(x^*,y^*)=left(x, frac7003-frac53cdot xright)$, where $0leq xleq 80$
So both solutions you mentioned are valid. But all solutions in between them as well.
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
$endgroup$
Your inequalities are right. Now see here how to solve the a linear program graphically. Below the picture shows the graph of your problem.
I got $Z_min$ min at two points (80,100) and (0, 700/3) the value of Zmin
in both cases is 700 now how do we chose between them ?
As you see at the graph that after the shift the objective function lies direcly on the first constraint $ygeq frac7003-frac53cdot x$. If we solve the objective function for y we get $y=fracz3-frac53cdot x$
The reason why the objective function lies directly on the first constraint is that both have the same slope of $-frac53$.
Thus the optimal solution is on every point on the constraint.
$(x^*,y^*)=left(x, frac7003-frac53cdot xright)$, where $0leq xleq 80$
So both solutions you mentioned are valid. But all solutions in between them as well.
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
answered Mar 13 at 13:44
callculuscallculus
18.5k31428
18.5k31428
$begingroup$
Thank you very much! Really appreciated, I learnt something new today
$endgroup$
– user74981
Mar 13 at 13:51
$begingroup$
@user74981 You are welcome. I´m glad that it helps.
$endgroup$
– callculus
Mar 13 at 13:53
add a comment |
$begingroup$
Thank you very much! Really appreciated, I learnt something new today
$endgroup$
– user74981
Mar 13 at 13:51
$begingroup$
@user74981 You are welcome. I´m glad that it helps.
$endgroup$
– callculus
Mar 13 at 13:53
$begingroup$
Thank you very much! Really appreciated, I learnt something new today
$endgroup$
– user74981
Mar 13 at 13:51
$begingroup$
Thank you very much! Really appreciated, I learnt something new today
$endgroup$
– user74981
Mar 13 at 13:51
$begingroup$
@user74981 You are welcome. I´m glad that it helps.
$endgroup$
– callculus
Mar 13 at 13:53
$begingroup$
@user74981 You are welcome. I´m glad that it helps.
$endgroup$
– callculus
Mar 13 at 13:53
add a comment |
user74981 is a new contributor. Be nice, and check out our Code of Conduct.
user74981 is a new contributor. Be nice, and check out our Code of Conduct.
user74981 is a new contributor. Be nice, and check out our Code of Conduct.
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1
$begingroup$
Aside from typing the raw text of your homework, what effort have you made ? Unless you say where you are blocked, this question will be closed...
$endgroup$
– Jean Marie
Mar 13 at 12:10
$begingroup$
@JeanMarie hey there I have tried this and actually wanted to attach it with the question but as I am new here and lack experience with this platform I am not able to, it says I need 10 notices or something to be able to post them my equations are 10x+6y greater than or = 1400 and 5x+10y greater than or = 1400
$endgroup$
– user74981
Mar 13 at 12:13
$begingroup$
@JeanMarie I am almost at the answer if there's any way I could post the picture so you guys could review it do let me know
$endgroup$
– user74981
Mar 13 at 12:16
$begingroup$
Very well. Each one of these inequalities (to which you should add $x geq 0$ and $y geq 0$) defines a half-plane : hatch each of them ; the quadrilateral region which is hatched four times is the "feasible region". Now take a moving line $ax+by=m$... that should be just touching the feasible region, as you have been taught, I assume in your lectures.
$endgroup$
– Jean Marie
Mar 13 at 12:19
$begingroup$
@JeanMarie I got Zmin min at two points (80,100) and (0, 700/3) the value of Zmin in both cases is 700 now how do we chose between them ? When both the points have same value
$endgroup$
– user74981
Mar 13 at 12:23