The budget constraint is p1x + p2y m, and a,b,, are all positive constants. Use the Lagrange and Kun-Tucker conditions. Find the demand function of x, for each utility function.

Utility Function

1 . u=ax+by

2 . u=min{x/a,y/b}

3. u=ln(x)+ln(y)

4. u = (x a)²(yb)²

5. u=ax+by

6. u=ax+by