Problem 3 (40 points) A single-product firm intends to produce 30 units of output as cheaply as possible. By using K units of capital and L units of labor, it can produce + L units. Suppose the prices of capital and labor are P1 and P20, respectively. The firm's problem is: minK + 201, = 30 Find the optimal choices of K and L. You will get points for specifying the: 1. 2. 3. 4. Lagrangean of the problem (Note: There is no need to convert the problem into a maximization of the negative of c(R, L).) First order necessary conditions Second order sufficient conditions (for local optimizer) Value of the objective function at (K , L')