Οperational Research And linear Programming-The Houses Builder Problem
EXERCISE
A builder has purchased $21,000$ square meters of land on which it is planned to build two types of houses, X(detached) and Y(a combination of town-house units), within an overall budget of $2100000$ euros.
A type X house costs $35000$ euros to build and requires $600$ square meters of land. A type Y house cost $60000$ euros to build and requires $300$ square meters of land.
To comply with local planning regulations, not more than $40$ buildings may be constructed on this land, but there must be at least five of each type. From past experience, it is known that the profit per type X house is about $10000$ euros and per type Y house to be about $6000$ euros.Profit is to maximized
QUESTION
The problem must be formulated in the form of linear programming and has to be solved in EXCEL by SOLVER. Based on this output, you have to state what the optimal solution is.
ATTEMPT
- Definition Of The Variables
X: Type X houses(Detached)
Y: Type Y houses(a combination of town-house units)
- Objective Function
Maximize problem(Profit is to maximized)
$$textrm{Max profit} =10000X + 6000Y$$
- Constraints
$X+Y leq 40$ (Not more than $40$ Buildings)
$600X+300Y leq 21000$(Square meters Constraint)
$35000X+60000Y leq 2100000$(Land requirements)
$X geq 5$ (At Least Five Of Each Type)
$Y geq 5$ (At Least Five Of Each Type)
So, when I get these constraints in my excel, Solver can't find a feasible solution and I don't know why. Is there any problem with my mathematical modelling? I believe that the constraints are obvious from the exercise!
This is my Formulation in Excel:
and this is the message when I use Solver to solve it and find MaxProf:
I would be really grateful if somebody can help me with this as it's important for the next questions of my project! Any thorough solution or explanation would be really helpful!
Thanks in advance!
optimization linear-programming mathematical-modeling
edited Dec 26 at 23:13
callculus
17.8k31427
asked Dec 26 at 12:52
Magic K. Mamba
316113
|
show 1 more comment
EXERCISE
A builder has purchased $21,000$ square meters of land on which it is planned to build two types of houses, X(detached) and Y(a combination of town-house units), within an overall budget of $2100000$ euros.
A type X house costs $35000$ euros to build and requires $600$ square meters of land. A type Y house cost $60000$ euros to build and requires $300$ square meters of land.
To comply with local planning regulations, not more than $40$ buildings may be constructed on this land, but there must be at least five of each type. From past experience, it is known that the profit per type X house is about $10000$ euros and per type Y house to be about $6000$ euros.Profit is to maximized
QUESTION
The problem must be formulated in the form of linear programming and has to be solved in EXCEL by SOLVER. Based on this output, you have to state what the optimal solution is.
ATTEMPT
- Definition Of The Variables
X: Type X houses(Detached)
Y: Type Y houses(a combination of town-house units)
- Objective Function
Maximize problem(Profit is to maximized)
$$textrm{Max profit} =10000X + 6000Y$$
- Constraints
$X+Y leq 40$ (Not more than $40$ Buildings)
$600X+300Y leq 21000$(Square meters Constraint)
$35000X+60000Y leq 2100000$(Land requirements)
$X geq 5$ (At Least Five Of Each Type)
$Y geq 5$ (At Least Five Of Each Type)
So, when I get these constraints in my excel, Solver can't find a feasible solution and I don't know why. Is there any problem with my mathematical modelling? I believe that the constraints are obvious from the exercise!
This is my Formulation in Excel:
and this is the message when I use Solver to solve it and find MaxProf:
I would be really grateful if somebody can help me with this as it's important for the next questions of my project! Any thorough solution or explanation would be really helpful!
Thanks in advance!
optimization linear-programming mathematical-modeling
edited Dec 26 at 23:13
callculus
17.8k31427
asked Dec 26 at 12:52
Magic K. Mamba
316113
I'm voting to close this question as off-topic because the question is not math related. Better site maybe super user meta.stackexchange.com/questions/155487/…
– mathcounterexamples.net
Dec 26 at 13:03
I´ve done the same in excel. It gave me the same message. It seems that the program is not feasible. Have you tried to sketch the feasible solution space?
– callculus
Dec 26 at 13:17
Υeah, but why? Did you use the same mathematical modelling as me? It seems impossible to me that the program is not feasible, because it's only the first question in my project. All the other questions depend on this question! Strange ha?
– Magic K. Mamba
Dec 26 at 13:26
@callculus yeah and I didn't find any feasible solution!
– Magic K. Mamba
Dec 26 at 13:31
It is clear that the problem has no solution. With a minimum of 5 houses of each, you don’t have enough land.
– mathcounterexamples.net
Dec 26 at 13:48
|
show 1 more comment
EXERCISE
A builder has purchased $21,000$ square meters of land on which it is planned to build two types of houses, X(detached) and Y(a combination of town-house units), within an overall budget of $2100000$ euros.
A type X house costs $35000$ euros to build and requires $600$ square meters of land. A type Y house cost $60000$ euros to build and requires $300$ square meters of land.
To comply with local planning regulations, not more than $40$ buildings may be constructed on this land, but there must be at least five of each type. From past experience, it is known that the profit per type X house is about $10000$ euros and per type Y house to be about $6000$ euros.Profit is to maximized
QUESTION
The problem must be formulated in the form of linear programming and has to be solved in EXCEL by SOLVER. Based on this output, you have to state what the optimal solution is.
ATTEMPT
- Definition Of The Variables
X: Type X houses(Detached)
Y: Type Y houses(a combination of town-house units)
- Objective Function
Maximize problem(Profit is to maximized)
$$textrm{Max profit} =10000X + 6000Y$$
- Constraints
$X+Y leq 40$ (Not more than $40$ Buildings)
$600X+300Y leq 21000$(Square meters Constraint)
$35000X+60000Y leq 2100000$(Land requirements)
$X geq 5$ (At Least Five Of Each Type)
$Y geq 5$ (At Least Five Of Each Type)
So, when I get these constraints in my excel, Solver can't find a feasible solution and I don't know why. Is there any problem with my mathematical modelling? I believe that the constraints are obvious from the exercise!
This is my Formulation in Excel:
and this is the message when I use Solver to solve it and find MaxProf:
I would be really grateful if somebody can help me with this as it's important for the next questions of my project! Any thorough solution or explanation would be really helpful!
Thanks in advance!
optimization linear-programming mathematical-modeling
edited Dec 26 at 23:13
callculus
17.8k31427
asked Dec 26 at 12:52
Magic K. Mamba
316113
EXERCISE
A builder has purchased $21,000$ square meters of land on which it is planned to build two types of houses, X(detached) and Y(a combination of town-house units), within an overall budget of $2100000$ euros.
A type X house costs $35000$ euros to build and requires $600$ square meters of land. A type Y house cost $60000$ euros to build and requires $300$ square meters of land.
To comply with local planning regulations, not more than $40$ buildings may be constructed on this land, but there must be at least five of each type. From past experience, it is known that the profit per type X house is about $10000$ euros and per type Y house to be about $6000$ euros.Profit is to maximized
QUESTION
The problem must be formulated in the form of linear programming and has to be solved in EXCEL by SOLVER. Based on this output, you have to state what the optimal solution is.
ATTEMPT
- Definition Of The Variables
X: Type X houses(Detached)
Y: Type Y houses(a combination of town-house units)
- Objective Function
Maximize problem(Profit is to maximized)
$$textrm{Max profit} =10000X + 6000Y$$
- Constraints
$X+Y leq 40$ (Not more than $40$ Buildings)
$600X+300Y leq 21000$(Square meters Constraint)
$35000X+60000Y leq 2100000$(Land requirements)
$X geq 5$ (At Least Five Of Each Type)
$Y geq 5$ (At Least Five Of Each Type)
So, when I get these constraints in my excel, Solver can't find a feasible solution and I don't know why. Is there any problem with my mathematical modelling? I believe that the constraints are obvious from the exercise!
This is my Formulation in Excel:
and this is the message when I use Solver to solve it and find MaxProf:
I would be really grateful if somebody can help me with this as it's important for the next questions of my project! Any thorough solution or explanation would be really helpful!
Thanks in advance!
optimization linear-programming mathematical-modeling
optimization linear-programming mathematical-modeling
edited Dec 26 at 23:13
callculus
17.8k31427
asked Dec 26 at 12:52
Magic K. Mamba
316113
edited Dec 26 at 23:13
callculus
17.8k31427
asked Dec 26 at 12:52
Magic K. Mamba
316113
edited Dec 26 at 23:13
callculus
17.8k31427
edited Dec 26 at 23:13
callculus
17.8k31427
edited Dec 26 at 23:13
callculus
17.8k31427
17.8k31427
asked Dec 26 at 12:52
Magic K. Mamba
316113
asked Dec 26 at 12:52
Magic K. Mamba
316113
asked Dec 26 at 12:52
Magic K. Mamba
316113
316113
I'm voting to close this question as off-topic because the question is not math related. Better site maybe super user meta.stackexchange.com/questions/155487/…
– mathcounterexamples.net
Dec 26 at 13:03
I´ve done the same in excel. It gave me the same message. It seems that the program is not feasible. Have you tried to sketch the feasible solution space?
– callculus
Dec 26 at 13:17
Υeah, but why? Did you use the same mathematical modelling as me? It seems impossible to me that the program is not feasible, because it's only the first question in my project. All the other questions depend on this question! Strange ha?
– Magic K. Mamba
Dec 26 at 13:26
@callculus yeah and I didn't find any feasible solution!
– Magic K. Mamba
Dec 26 at 13:31
It is clear that the problem has no solution. With a minimum of 5 houses of each, you don’t have enough land.
– mathcounterexamples.net
Dec 26 at 13:48
|
show 1 more comment
I'm voting to close this question as off-topic because the question is not math related. Better site maybe super user meta.stackexchange.com/questions/155487/…
– mathcounterexamples.net
Dec 26 at 13:03
I´ve done the same in excel. It gave me the same message. It seems that the program is not feasible. Have you tried to sketch the feasible solution space?
– callculus
Dec 26 at 13:17
Υeah, but why? Did you use the same mathematical modelling as me? It seems impossible to me that the program is not feasible, because it's only the first question in my project. All the other questions depend on this question! Strange ha?
– Magic K. Mamba
Dec 26 at 13:26
@callculus yeah and I didn't find any feasible solution!
– Magic K. Mamba
Dec 26 at 13:31
It is clear that the problem has no solution. With a minimum of 5 houses of each, you don’t have enough land.
– mathcounterexamples.net
Dec 26 at 13:48
I'm voting to close this question as off-topic because the question is not math related. Better site maybe super user meta.stackexchange.com/questions/155487/…
– mathcounterexamples.net
Dec 26 at 13:03
I'm voting to close this question as off-topic because the question is not math related. Better site maybe super user meta.stackexchange.com/questions/155487/…
– mathcounterexamples.net
Dec 26 at 13:03
I´ve done the same in excel. It gave me the same message. It seems that the program is not feasible. Have you tried to sketch the feasible solution space?
– callculus
Dec 26 at 13:17
I´ve done the same in excel. It gave me the same message. It seems that the program is not feasible. Have you tried to sketch the feasible solution space?
– callculus
Dec 26 at 13:17
Υeah, but why? Did you use the same mathematical modelling as me? It seems impossible to me that the program is not feasible, because it's only the first question in my project. All the other questions depend on this question! Strange ha?
– Magic K. Mamba
Dec 26 at 13:26
Υeah, but why? Did you use the same mathematical modelling as me? It seems impossible to me that the program is not feasible, because it's only the first question in my project. All the other questions depend on this question! Strange ha?
– Magic K. Mamba
Dec 26 at 13:26
@callculus yeah and I didn't find any feasible solution!
– Magic K. Mamba
Dec 26 at 13:31
@callculus yeah and I didn't find any feasible solution!
– Magic K. Mamba
Dec 26 at 13:31
It is clear that the problem has no solution. With a minimum of 5 houses of each, you don’t have enough land.
– mathcounterexamples.net
Dec 26 at 13:48
It is clear that the problem has no solution. With a minimum of 5 houses of each, you don’t have enough land.
– mathcounterexamples.net
Dec 26 at 13:48
|
show 1 more comment
1 Answer
1
active
oldest
votes
You have made a typo at the exercise. $text{It is "A builder has purchased 21,00}$ $color{red}{0}$ $text{square meters of land}$ $text{on which it is planned to build... "}$
But you have written it at your constraint: $600X+300Y leq 21,000 $ (Square meters Constraint)
If you use this constraint the problem is feasible. This is what I got by using the Excel solver:
Excel sheet with formulas
Input mask
answered Dec 26 at 14:02
callculus
17.8k31427
1
This is after using Solver?I use Sumproduct function,not Sum!Is this wrong?And what is these $1050000$ and $600000$??From where did you get these?
– Magic K. Mamba
Dec 26 at 14:07
It is $30cdot 35000=1,050,000$ for instance. And similar for y: $10cdot 60,000=600,000$
– callculus
Dec 26 at 14:10
So,i made mistake with the variables.I use 1 and 1 but that's wrong because i have a constraint that tells me that i have $Y geq 5$ and $X geq 5$.Right?
– Magic K. Mamba
Dec 26 at 14:12
And why you use Sum function?
– Magic K. Mamba
Dec 26 at 14:14
1
No problem. We are here to help, especially on Christmas. Yeah, I´ve used the solver.
– callculus
Dec 26 at 14:25
|
show 17 more comments
Your Answer
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1 Answer
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You have made a typo at the exercise. $text{It is "A builder has purchased 21,00}$ $color{red}{0}$ $text{square meters of land}$ $text{on which it is planned to build... "}$
But you have written it at your constraint: $600X+300Y leq 21,000 $ (Square meters Constraint)
If you use this constraint the problem is feasible. This is what I got by using the Excel solver:
Excel sheet with formulas
Input mask
answered Dec 26 at 14:02
callculus
17.8k31427
1
This is after using Solver?I use Sumproduct function,not Sum!Is this wrong?And what is these $1050000$ and $600000$??From where did you get these?
– Magic K. Mamba
Dec 26 at 14:07
It is $30cdot 35000=1,050,000$ for instance. And similar for y: $10cdot 60,000=600,000$
– callculus
Dec 26 at 14:10
So,i made mistake with the variables.I use 1 and 1 but that's wrong because i have a constraint that tells me that i have $Y geq 5$ and $X geq 5$.Right?
– Magic K. Mamba
Dec 26 at 14:12
And why you use Sum function?
– Magic K. Mamba
Dec 26 at 14:14
1
No problem. We are here to help, especially on Christmas. Yeah, I´ve used the solver.
– callculus
Dec 26 at 14:25
|
show 17 more comments
You have made a typo at the exercise. $text{It is "A builder has purchased 21,00}$ $color{red}{0}$ $text{square meters of land}$ $text{on which it is planned to build... "}$
But you have written it at your constraint: $600X+300Y leq 21,000 $ (Square meters Constraint)
If you use this constraint the problem is feasible. This is what I got by using the Excel solver:
Excel sheet with formulas
Input mask
answered Dec 26 at 14:02
callculus
17.8k31427
1
This is after using Solver?I use Sumproduct function,not Sum!Is this wrong?And what is these $1050000$ and $600000$??From where did you get these?
– Magic K. Mamba
Dec 26 at 14:07
It is $30cdot 35000=1,050,000$ for instance. And similar for y: $10cdot 60,000=600,000$
– callculus
Dec 26 at 14:10
So,i made mistake with the variables.I use 1 and 1 but that's wrong because i have a constraint that tells me that i have $Y geq 5$ and $X geq 5$.Right?
– Magic K. Mamba
Dec 26 at 14:12
And why you use Sum function?
– Magic K. Mamba
Dec 26 at 14:14
1
No problem. We are here to help, especially on Christmas. Yeah, I´ve used the solver.
– callculus
Dec 26 at 14:25
|
show 17 more comments
You have made a typo at the exercise. $text{It is "A builder has purchased 21,00}$ $color{red}{0}$ $text{square meters of land}$ $text{on which it is planned to build... "}$
But you have written it at your constraint: $600X+300Y leq 21,000 $ (Square meters Constraint)
If you use this constraint the problem is feasible. This is what I got by using the Excel solver:
Excel sheet with formulas
Input mask
answered Dec 26 at 14:02
callculus
17.8k31427
You have made a typo at the exercise. $text{It is "A builder has purchased 21,00}$ $color{red}{0}$ $text{square meters of land}$ $text{on which it is planned to build... "}$
But you have written it at your constraint: $600X+300Y leq 21,000 $ (Square meters Constraint)
If you use this constraint the problem is feasible. This is what I got by using the Excel solver:
Excel sheet with formulas
Input mask
answered Dec 26 at 14:02
callculus
17.8k31427
edited Dec 26 at 14:45
answered Dec 26 at 14:02
callculus
17.8k31427
answered Dec 26 at 14:02
callculus
17.8k31427
answered Dec 26 at 14:02
callculus
17.8k31427
17.8k31427
1
This is after using Solver?I use Sumproduct function,not Sum!Is this wrong?And what is these $1050000$ and $600000$??From where did you get these?
– Magic K. Mamba
Dec 26 at 14:07
It is $30cdot 35000=1,050,000$ for instance. And similar for y: $10cdot 60,000=600,000$
– callculus
Dec 26 at 14:10
So,i made mistake with the variables.I use 1 and 1 but that's wrong because i have a constraint that tells me that i have $Y geq 5$ and $X geq 5$.Right?
– Magic K. Mamba
Dec 26 at 14:12
And why you use Sum function?
– Magic K. Mamba
Dec 26 at 14:14
1
No problem. We are here to help, especially on Christmas. Yeah, I´ve used the solver.
– callculus
Dec 26 at 14:25
|
show 17 more comments
1
This is after using Solver?I use Sumproduct function,not Sum!Is this wrong?And what is these $1050000$ and $600000$??From where did you get these?
– Magic K. Mamba
Dec 26 at 14:07
It is $30cdot 35000=1,050,000$ for instance. And similar for y: $10cdot 60,000=600,000$
– callculus
Dec 26 at 14:10
So,i made mistake with the variables.I use 1 and 1 but that's wrong because i have a constraint that tells me that i have $Y geq 5$ and $X geq 5$.Right?
– Magic K. Mamba
Dec 26 at 14:12
And why you use Sum function?
– Magic K. Mamba
Dec 26 at 14:14
1
No problem. We are here to help, especially on Christmas. Yeah, I´ve used the solver.
– callculus
Dec 26 at 14:25
1
1
This is after using Solver?I use Sumproduct function,not Sum!Is this wrong?And what is these $1050000$ and $600000$??From where did you get these?
– Magic K. Mamba
Dec 26 at 14:07
This is after using Solver?I use Sumproduct function,not Sum!Is this wrong?And what is these $1050000$ and $600000$??From where did you get these?
– Magic K. Mamba
Dec 26 at 14:07
It is $30cdot 35000=1,050,000$ for instance. And similar for y: $10cdot 60,000=600,000$
– callculus
Dec 26 at 14:10
It is $30cdot 35000=1,050,000$ for instance. And similar for y: $10cdot 60,000=600,000$
– callculus
Dec 26 at 14:10
So,i made mistake with the variables.I use 1 and 1 but that's wrong because i have a constraint that tells me that i have $Y geq 5$ and $X geq 5$.Right?
– Magic K. Mamba
Dec 26 at 14:12
So,i made mistake with the variables.I use 1 and 1 but that's wrong because i have a constraint that tells me that i have $Y geq 5$ and $X geq 5$.Right?
– Magic K. Mamba
Dec 26 at 14:12
And why you use Sum function?
– Magic K. Mamba
Dec 26 at 14:14
And why you use Sum function?
– Magic K. Mamba
Dec 26 at 14:14
1
1
No problem. We are here to help, especially on Christmas. Yeah, I´ve used the solver.
– callculus
Dec 26 at 14:25
No problem. We are here to help, especially on Christmas. Yeah, I´ve used the solver.
– callculus
Dec 26 at 14:25
|
show 17 more comments
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I'm voting to close this question as off-topic because the question is not math related. Better site maybe super user meta.stackexchange.com/questions/155487/…
– mathcounterexamples.net
Dec 26 at 13:03
I´ve done the same in excel. It gave me the same message. It seems that the program is not feasible. Have you tried to sketch the feasible solution space?
– callculus
Dec 26 at 13:17
Υeah, but why? Did you use the same mathematical modelling as me? It seems impossible to me that the program is not feasible, because it's only the first question in my project. All the other questions depend on this question! Strange ha?
– Magic K. Mamba
Dec 26 at 13:26
@callculus yeah and I didn't find any feasible solution!
– Magic K. Mamba
Dec 26 at 13:31
It is clear that the problem has no solution. With a minimum of 5 houses of each, you don’t have enough land.
– mathcounterexamples.net
Dec 26 at 13:48