# Quadratic equation solving with constraint.

1. Oct 28, 2012

### qwerty11

1. The problem statement, all variables and given/known data
So I've worked this problem for awhile. Its a several page of math problem with optimization, legrangians, cramers rule, etc to get to this point. All I need to do now is by hand solve this equation for x and y with the constraint.

2. Relevant equations

-0.03x^2 + 40x - 0.02y^2 + 5y+ 55000 = 0
Subject to the constraint: x+y=3000

3. The attempt at a solution

I could put up the pages of work I've done to get to this point, but it really doesn't have any relevant info to help get to this point. I have the answers which is x=1100 & y=1900. Just don't know how to do this last step I've got to.

Thanks so much for the help!

Last edited by a moderator: Oct 28, 2012
2. Oct 28, 2012

### Mentallic

If your constraint is x+y=3000 then you just need to plug y = 3000-x into the quadratic.

Last edited by a moderator: Oct 28, 2012
3. Oct 28, 2012

### Staff: Mentor

Geometrically, the quadratic equation in x and y represents an ellipse, and the constraint represents a straight line, so you will either get no solutions, one solution, or two solutions.

4. Oct 29, 2012

### qwerty11

Thanks so much! This is exactly what was messing me up. Dono why I didn't think of that.

Thanks again!

5. Oct 29, 2012

### Mentallic

You're welcome