Suppose that Q = min(2K, L) is the production function of a firm.
The firm wishes to minimize the cost of attaining an output level of 100. Let the wage rate be w = 4 and the rental rate of capital be r = 1. What is the cost minimizing combination of labor and capital, (L∗,K∗)? What is the minimum cost to produce 100 units of output?
SIMILAR AS CONSUMER THEORY for perfect complements. Tangent condition becomes that 2K and L are both set equal to the desired level of output, Q.