what is the optimal condition of u(x1,x2) = ln(x1) + (x2)/2
To find the optimal condition of the function u(x1, x2) = ln(x1) + (x2)/2, we need to find the values of x1 and x2 that maximize or minimize the function.
To do this, we can take partial derivatives of the function with respect to x1 and x2 and set them equal to zero.
∂u/∂x1 = 1/x1 = 0
∂u/∂x2 = 1/2 = 0
However, we cannot set 1/x1 = 0 because it results in an undefined value. Therefore, there is no optimal condition for the function u(x1, x2) = ln(x1) + (x2)/2.
To find the optimal condition of the function u(x1, x2) = ln(x1) + (x2)/2, we need to find the values of x1 and x2 that maximize or minimize the function.
To do this, we can take the partial derivatives of u with respect to x1 and x2 and set them equal to zero.
1. Partial derivative with respect to x1:
∂u/∂x1 = 1/x1 = 0
Setting this equal to zero, we find that x1 = 0 is not defined for ln(x1), so there is no critical point or maximum/minimum in this direction.
2. Partial derivative with respect to x2:
∂u/∂x2 = 1/2 = 0
Setting this equal to zero, we find that x2 = 0.
Therefore, the optimal condition for u(x1, x2) = ln(x1) + (x2)/2 is x2 = 0. The function does not have a critical point in the x1 direction.