Constraint Optimization:

A producer produces the shoe (Q), using the labor (L) and capital (K), and the production function follows the following form as: Q=10K21L21 The per unit price of capital and labor are 1 USD and 4 USD respectively, and the production capacity of this firm equals to 16 units. A. Explain the concept of constrained optimization. Given the information, construct the firm's optimization problem. B. Estimate the amount of labor and capital that will satisfy the maximum output. C. Using the second order condition, construct the Bordered Hessian Matrix, and prove that Hessian matrix follows the negative semi-definite matrix. A producer produces the shoe (Q), using the labor (L) and capital (K), and the production function follows the following form as: Q=10K21L21 The per unit price of capital and labor are 1 USD and 4 USD respectively, and the production capacity of this firm equals to 16 units. A. Explain the concept of constrained optimization. Given the information, construct the firm's optimization problem. B. Estimate the amount of labor and capital that will satisfy the maximum output. C. Using the second order condition, construct the Bordered Hessian Matrix, and prove that Hessian matrix follows the negative semi-definite matrix