Business calculus. Can you show me hand written work.

A manufacturer's production is modeled by the Cobb-Douglas function: f (x, y) = 100x y where x represents the units of labor (at $150 per unit) and y represents the units of capital (at $250 per unit). The total costs for labor and capital cannot exceed $50,000. Will the manufacturer's maximum production level exceed 16,000 units? (Hint: It's not a regular max/min problem - this one has constraints! Hence? Lagrange Multiplier time!)