A manufacturer's total production of a new product is P(L, K) = 1200L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and capital is $480,000. (a) To maximize production, how much should be spent on labor? $  160000       How much on capital? $  320000       (b) Find the value of the Lagrange multiplier. 252

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