Optimization Problem

[Dari]

We are allowed to use excel to figure problems like this out but there will not be any computers allowed in the final exam. But I have this problem I cannot figure out by hand. Anyone want to take a stab at it?

1. 0.0169A^2 + 0.04B^2 + 0.052AB = 0.0225

2. 0.07A + 0.11B + 0.04 = R

I'm trying to maximize the second equation (R) but How can I put the first equation into it?

 

[Jhill]

When you said you had to maximize the 2nd equation I thought of this.

http://www.hemmy.net/2006/07/19/funny-algebra-answer/

 

[Born2bwire]

Parameterize the first equation. Substitute into the second. Take the derivative and solve for the condition for a maximum. Then substitute back into your parametric equations.

 

[Dari]

By the way, the original constraints were:

1. 0.0169A^2 + 0.04B^2 + 0.052AB = 0.0225

2. A + B + C = 1

3. 0.11A + 0.15B + 0.04C = R

 

[Dari]

Originally posted by: Born2bwire
Parameterize the first equation. Substitute into the second. Take the derivative and solve for the condition for a maximum. Then substitute back into your parametric equations.

How do I go about parametrizing the first equation? You mean like A = 1+t, Y = ...etc?

Oh, the first one is in the form of an ellipse, right?

 

[Born2bwire]

Originally posted by: Dari

Originally posted by: Born2bwire
Parameterize the first equation. Substitute into the second. Take the derivative and solve for the condition for a maximum. Then substitute back into your parametric equations.

How do I go about parametrizing the first equation? You mean like A = 1+t, Y = ...etc?

Exactly. You should be able to see what geometric shape that is being described in the first equation.

 

[Dari]

Originally posted by: Born2bwire

Originally posted by: Dari

Originally posted by: Born2bwire
Parameterize the first equation. Substitute into the second. Take the derivative and solve for the condition for a maximum. Then substitute back into your parametric equations.

How do I go about parametrizing the first equation? You mean like A = 1+t, Y = ...etc?

Exactly. You should be able to see what geometric shape that is being described in the first equation.

an ellipse?

 

[Born2bwire]

Originally posted by: Dari

Originally posted by: Born2bwire

Originally posted by: Dari

Originally posted by: Born2bwire
Parameterize the first equation. Substitute into the second. Take the derivative and solve for the condition for a maximum. Then substitute back into your parametric equations.

How do I go about parametrizing the first equation? You mean like A = 1+t, Y = ...etc?

Exactly. You should be able to see what geometric shape that is being described in the first equation.

an ellipse?

Whoops, made a mental mistake there. Nah, while you can make into a perfect square easily it isn't a geometric shape of merit. Meh, well another way of doing it would be to solve for A or B in equation one and then substitute it into the second equation. Same thing but at first I thought it was a circle or ellipse in which case a parametric form would be easy to spit out but a second look at it shows that this isn't the case.

 

[Random Variable]

lagrange multipliers

 

[Dari]

I haven't a clue as how to isolate A or B in equation 1.

 

[Dari]

Originally posted by: Random Variable
lagrange multipliers

That's what I thought as well, but how do I set it up? How do I set up a Kuhn-Tucker set of equations?

 

[Random Variable]

What's the original problem?

 

[Dari]

Originally posted by: Random Variable
What's the original problem?

It's a finance problem and the equations were spelled out in my second post. However, for equation 1, we want a less than or equal to (.0225) instead of a simple "=". I also want to maximize equation 3.

 

[Born2bwire]

Originally posted by: Dari
I haven't a clue as how to isolate A or B in equation 1.

Reduce the LHS of equation 1 and solve for A in terms of B. You remember perfect squares right?

 

[Modeps]

I'm so happy I'm not in school anymore.

 

[Dari]

Originally posted by: Born2bwire

Originally posted by: Dari
I haven't a clue as how to isolate A or B in equation 1.

Reduce the LHS of equation 1 and solve for A in terms of B. You remember perfect squares right?

Perfect squares? No, I don't remember them.

 

[Dari]

Wow, it is a perfect square.

Thanks a lot, man

 

[Born2bwire]

Originally posted by: Dari

Originally posted by: Born2bwire

Originally posted by: Dari
I haven't a clue as how to isolate A or B in equation 1.

Reduce the LHS of equation 1 and solve for A in terms of B. You remember perfect squares right?

Perfect squares? No, I don't remember them.

Take a look at the expansion of the square of the sum of two numbers. You may also recall doing things like "completing the square" but in this case it is not necessary.

 

[Dari]

Originally posted by: Born2bwire

Originally posted by: Dari

Originally posted by: Born2bwire

Originally posted by: Dari
I haven't a clue as how to isolate A or B in equation 1.

Reduce the LHS of equation 1 and solve for A in terms of B. You remember perfect squares right?

Perfect squares? No, I don't remember them.

Take a look at the expansion of the square of the sum of two numbers. You may also recall doing things like "completing the square" but in this case it is not necessary.

It is a perfect square, making my job a whole lot easier.