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Question 6 (17 points) A manufacturing company specializes in producing high-quality electronics. The company's production function is = L%?K%, where L represents the hours of labor and K represents the number of machines used. The company aims to minimize its production costs for a target output g, given that the wage rate for labor is w per hour and the rental rate for machines is r per unit. a) (4 points) Construct the Lagrangian expression for the company's cost minimization problem, incorporating the given production function, wage rate, and rental rate. b) (5 points) Derive the first-order conditions from the Lagrangian for finding the optimal levels of labor (L) and machines (K) that minimize cost. ) (4 points) Calculate the cost-minimizing L and K to achieve the target production d) (4 points) Assuming the government offers a subsidy of $10 per machine, recalculate the optimal levels of labor and machines. -Page 2- Question 7. (17 points). Jeremy is running a business and his production function is: g = 20L%5K. Jeremy is able to accumulate $10,000 to finance the business. Workers cost $10 per unit and capital costs $50 per unit. a. (13 points) If Jeremy wishes to produce the most output with the finances available, how much labor and capital should he employ? Use a Lagrangian for output maximization to solve this problem. b. (4 points) Does this bundle of capital and labor also minimize the costs