$\lambda$ -Ranger Construction Is Preparing to Repair Potholes, Under Contract to to the Local

$\lambda$
-Ranger Construction is preparing to repair potholes, under contract to the local county road repair agency. Based on past experience, Ranger has found that output can be described by: Q = K^.5L^.5, where Q = pot holes filled, K = units of capital, and L = units of labor. Ranger can hire labor at $12 per hour, and the cost of capital is $8 per unit. Capacity limitations require that Ranger accepts no more than $96,000 worth of filling this season. What is the optimal mix of inputs for Ranger? How many potholes should Ranger agree to fill? Use the method of Lagrange multipliers to find the solution.