Help solving for 3 equations and 3 unknowns

[skybox]

Homework Statement

Solve the following equation for [itex]P_{1}[/itex] and [itex]P_{2}[/itex]

Homework Equations

[itex]7.0+0.004P_{1}-\lambda(1-0.0004P_{1})=0[/itex]
[itex]7.0+0.004P_{2}-\lambda=0[/itex]
[itex]P_{1}+P_{2}-500-0.0002P_{1}^{2}=0[/itex]

The Attempt at a Solution

I am having some issues on ways to solve this problem. I guess the main point I am stuck on is how do I even approach it?

I have three unknowns [itex]P_{1}, P_{2}, \lambda[/itex] and three equations, so I should be able to solve for [itex]P_{1}, P_{2} [/itex].

The example shows that the solutions are:
[itex]P_{1}=178.882 , P_{2}=327.496[/itex].

Any suggestions or tips would be greatly appreciated

 

[skiller]

My first suggestion would be to give some equations. You've given 3 expressions, which don't appear to equate to anything.

 

[skybox]

My first suggestion would be to give some equations. You've given 3 expressions, which don't appear to equate to anything.

Woops. Updated. All expressions equal 0

 

[skiller]

Woops. Updated. All expressions equal 0

That's better!

How are you with algebraic manipulation?

The first equation gives you [itex]P_1[/itex] in terms of [itex]\lambda[/itex], and the second gives [itex]P_2[/itex] in terms of [itex]\lambda[/itex].

Plug them both into the third equation and you find the value of [itex]\lambda[/itex].

Use this value of [itex]\lambda[/itex] to find the values of [itex]P_1[/itex] and [itex]P_2[/itex].

Job done!

 

[skybox]

That's better!

How are you with algebraic manipulation?

The first equation gives you [itex]P_1[/itex] in terms of [itex]\lambda[/itex], and the second gives [itex]P_2[/itex] in terms of [itex]\lambda[/itex].

Plug them both into the third equation and you find the value of [itex]\lambda[/itex].

Use this value of [itex]\lambda[/itex] to find the values of [itex]P_1[/itex] and [itex]P_2[/itex].

Job done!

Thanks for the help. This is becoming a very complicated solution :S Will just use Matlab to solve!