• Use the method of Lagrange multipliers to solve optimization problems with one constraint. Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 80L0.84 K0.16 where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $400 and each unit of capital costs $2,000. Further suppose a total of $250,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint? Units of labor, L = Units of capital, K = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production = units

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A: According  to guidelines  we solve one question. Thanku

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A: Given Utility Function :  U(x, z) = 3x2 + z2 - 2xz Px = Py = $1 Total Income = $1000

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A: Approach to solving the question: Step 1: Define the Objective Function The initial stage entails…