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Use Lagrange multipliers to find the maximum production level when the total cost of labor (at...

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

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