In: Math
Use Lagrange multipliers to find the maximum production level when the total cost of labor (at $111 per unit) and capital (at $50 per unit) is limited to $250,000, where P is the production function, x is the number of units of labor, and y is the number of units of capital. (Round your answer to the nearest whole number.) (Please use the numbers given I've followed other 'solutions' and keep getting the wrong answer, I just want to see that the method used in response gets the correct answer and how.)
P(x, y) = 100x0.25y0.75