The total production P of a certain product depends on the amount L of labor used and the amount K of capital investment Cobb Douglas model P bL K 1 follows from certain economic assumptions, where b and are positive constants and 1 If the cost of a unit of labor is m and the cost of a unit of capi...

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The total production P of a certain product depends on the amount L of labor used and

Question:

The total production P of a certain product depends on the amount L of labor used and the amount K of capital investment. Cobb-Douglas model P = bL^αK^1−α follows from certain economic assumptions, where b and α are positive constants and α < 1. If the cost of a unit of labor is m and the cost of a unit of capital is n, and the company can spend only p dollars as its total budget, then maximizing the production P is subject to the constraint mL + nK = p. Show that the maximum production occurs when