Quadratic equation solving with constraint.

[qwerty11]

Homework Statement

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.

Homework Equations

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

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!

 

[Mentallic]

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

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

 

[Mark44]

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.

 

[qwerty11]

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

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

Thanks again!

 

[Mentallic]

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

Thanks again!

You're welcome