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Solving linear Programming problem with simplex method.

Solving linear programming problem with global opt methodLinear Programming - Simplex MethodSimplex Method issues solving this problemLP Constraint ProblemLinear programming problem using the simplex algorithm, dual problem…solving minimum linear programming with simplex methodHelp solving linear programming problem with simplex methodSolving linear programming with bounds by simplex algorithmWhy is my linear programming model wrong?Linear Programming Simplex Method: How to pick leaving variable

1

$begingroup$

I have tried this question but can't come up with a maximization answer. I am not certain where I am wrong but I think my equations have an issue, you can't take look at them below the question.
The questions states,
An investor has to invest in an economy and has three options to invest in: banking, insurance and manufacturing. The return on investment is 20%, 25% and 15% respectively. The president said that he must invest the investment in banking should not exceed twice the total investment in insurance and manufacturing by more than 3 million dollars. At the same time not less than 30% of the investment should be in manufacturing. If the total money available to the investor is 18 million dollars.

a) Formulate his problem as an LP problem

b) Use the simplex table to calculate the maximum profit he can make.

NB:
Hint: Let the money, in million dollars invested in banking be $x_1$ , in insurance be $x_2 $ and in manufacturing be $x_3$ .

In my solution, i managed to come up with my objective function as
$x_1 + x_2 + x_3 = 18$
and with the constraints I came up with;

(x1 <= x2)....eqn1-(president said that he must invest the investment in banking should not exceed twice the total investment in insurance)

(x1 + 3 <= x3)....eqn2-(manufacturing by more than 3 million dollars)

(x3 >= (30% * 18million))...eqn3-(At the same time not less than 30% of the investment should be in manufacturing.)

From the equations i started iterating and stuff isen't just adding up somewhere. SOMEONE HELP.

linear-programming

share|cite|improve this question

edited Mar 22 at 11:12

dmtri

1,7712521

asked Mar 22 at 10:41

andy lacronandy lacron

61

$endgroup$

add a comment | 

1

$begingroup$

I have tried this question but can't come up with a maximization answer. I am not certain where I am wrong but I think my equations have an issue, you can't take look at them below the question.
The questions states,
An investor has to invest in an economy and has three options to invest in: banking, insurance and manufacturing. The return on investment is 20%, 25% and 15% respectively. The president said that he must invest the investment in banking should not exceed twice the total investment in insurance and manufacturing by more than 3 million dollars. At the same time not less than 30% of the investment should be in manufacturing. If the total money available to the investor is 18 million dollars.

a) Formulate his problem as an LP problem

b) Use the simplex table to calculate the maximum profit he can make.

NB:
Hint: Let the money, in million dollars invested in banking be $x_1$ , in insurance be $x_2 $ and in manufacturing be $x_3$ .

In my solution, i managed to come up with my objective function as
$x_1 + x_2 + x_3 = 18$
and with the constraints I came up with;

(x1 <= x2)....eqn1-(president said that he must invest the investment in banking should not exceed twice the total investment in insurance)

(x1 + 3 <= x3)....eqn2-(manufacturing by more than 3 million dollars)

(x3 >= (30% * 18million))...eqn3-(At the same time not less than 30% of the investment should be in manufacturing.)

From the equations i started iterating and stuff isen't just adding up somewhere. SOMEONE HELP.

linear-programming

share|cite|improve this question

edited Mar 22 at 11:12

dmtri

1,7712521

asked Mar 22 at 10:41

andy lacronandy lacron

61

$endgroup$

add a comment | 

$begingroup$

I have tried this question but can't come up with a maximization answer. I am not certain where I am wrong but I think my equations have an issue, you can't take look at them below the question.
The questions states,
An investor has to invest in an economy and has three options to invest in: banking, insurance and manufacturing. The return on investment is 20%, 25% and 15% respectively. The president said that he must invest the investment in banking should not exceed twice the total investment in insurance and manufacturing by more than 3 million dollars. At the same time not less than 30% of the investment should be in manufacturing. If the total money available to the investor is 18 million dollars.

a) Formulate his problem as an LP problem

b) Use the simplex table to calculate the maximum profit he can make.

NB:
Hint: Let the money, in million dollars invested in banking be $x_1$ , in insurance be $x_2 $ and in manufacturing be $x_3$ .

In my solution, i managed to come up with my objective function as
$x_1 + x_2 + x_3 = 18$
and with the constraints I came up with;

(x1 <= x2)....eqn1-(president said that he must invest the investment in banking should not exceed twice the total investment in insurance)

(x1 + 3 <= x3)....eqn2-(manufacturing by more than 3 million dollars)

(x3 >= (30% * 18million))...eqn3-(At the same time not less than 30% of the investment should be in manufacturing.)

From the equations i started iterating and stuff isen't just adding up somewhere. SOMEONE HELP.

linear-programming

share|cite|improve this question

edited Mar 22 at 11:12

dmtri

1,7712521

asked Mar 22 at 10:41

andy lacronandy lacron

61

$endgroup$

share|cite|improve this question

edited Mar 22 at 11:12

dmtri

1,7712521

asked Mar 22 at 10:41

andy lacronandy lacron

61

share|cite|improve this question

edited Mar 22 at 11:12

dmtri

1,7712521

asked Mar 22 at 10:41

andy lacronandy lacron

61

edited Mar 22 at 11:12

dmtri

1,7712521

edited Mar 22 at 11:12

dmtri

1,7712521

asked Mar 22 at 10:41

andy lacronandy lacron

61

asked Mar 22 at 10:41

andy lacronandy lacron

61

1 Answer
1

active

oldest

votes

1

$begingroup$

The objective function you are using is incorrect. You want to maximise the profit, which you can formulate as $0.2x_1 + 0.25x_2 + 0.15x_3$. The equation you are currently using as the objective is actually another constraint.

You should also remember that in order to use the simplex method, you should bring your LP into the standard form.

share|cite|improve this answer

edited Mar 22 at 11:29

answered Mar 22 at 11:20

wiluqawiluqa

365

$endgroup$

add a comment | 

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1

$begingroup$

The objective function you are using is incorrect. You want to maximise the profit, which you can formulate as $0.2x_1 + 0.25x_2 + 0.15x_3$. The equation you are currently using as the objective is actually another constraint.

You should also remember that in order to use the simplex method, you should bring your LP into the standard form.

share|cite|improve this answer

edited Mar 22 at 11:29

answered Mar 22 at 11:20

wiluqawiluqa

365

$endgroup$

add a comment | 

1

$begingroup$

The objective function you are using is incorrect. You want to maximise the profit, which you can formulate as $0.2x_1 + 0.25x_2 + 0.15x_3$. The equation you are currently using as the objective is actually another constraint.

You should also remember that in order to use the simplex method, you should bring your LP into the standard form.

share|cite|improve this answer

edited Mar 22 at 11:29

answered Mar 22 at 11:20

wiluqawiluqa

365

$endgroup$

add a comment | 

$begingroup$

The objective function you are using is incorrect. You want to maximise the profit, which you can formulate as $0.2x_1 + 0.25x_2 + 0.15x_3$. The equation you are currently using as the objective is actually another constraint.

You should also remember that in order to use the simplex method, you should bring your LP into the standard form.

share|cite|improve this answer

edited Mar 22 at 11:29

answered Mar 22 at 11:20

wiluqawiluqa

365

$endgroup$

share|cite|improve this answer

edited Mar 22 at 11:29

answered Mar 22 at 11:20

wiluqawiluqa

365

answered Mar 22 at 11:20

wiluqawiluqa

365

answered Mar 22 at 11:20

wiluqawiluqa

365