A paint manufacturing company has a production function Q = 2K + 2L^1/2 .

a. Use the Lagrangian method to derive the input demand functions for L and K for an interior optimum.

b. What is the cost-minimizing input combination to produce 100 units of output if the firm faces input prices w= 1 and r =50? Draw an isoquant-isocost diagram and show your cost-minimizing bundle. c. Verify that the firm's cost-minimizing input combination to produce Q = 100 involves no use of capital when r = 110 keeping w = $1. What is the amount of labor the firm would use in this situation? d. In part ( c ), is MRTS equal to the input price ratio? If not, does it make sense that the equality is not satisfied at the optimal bundle?