I couldn't solve some of the problems

--If the solution to the utility maximizing problem max u(x, y) = xy subject to x + 3y = 150 is (x*, y*), then y* is:

(I got 30 on this one, but I am not sure.)

--If the solution to the utility maximizing problem max u(x, y) = xy + 200x + 100y subject to 3x + 4y = 1000 is (x*, y*), then x* is

--If the solution to the utility maximizing problem max u(x, y) = ln x + ln y subject to px + qy = m is (x*, y*), then x* + y* is:

And the last problem with economic application:

A consumer has a utility function u(x,y) = x.25y.75 . The consumer has $100 to spend. Px =$10, Py = $20. What would the Langragian be here? and the Lx, Ly, Lz...? I'm clueless how to solve these, the professor is usually very basic, this is not even in the book. Thank you. 2. I found a different answer to the first problem when I made the substitution$\displaystyle u(x,y)=xy=(150-3y)y=150y-3y^2.$Differentiating, I obtained$\displaystyle u'(x,y)=150-6y,$which equals$\displaystyle 0$when$\displaystyle y=25.\$