Final answer:
To maximize production, find the values of L and K that yield the highest output by taking partial derivatives of the production function with respect to L and K, setting them equal to zero, and evaluating the second partial derivatives to determine if they are maximums or minimums. The corresponding level of production can be obtained by substituting the values of L and K into the production function.
Step-by-step explanation:
The production function Q = f[L, K] represents the relationship between the quantities of inputs labor (L) and capital (K) and the level of production (Q). To maximize production, we need to find the values of L and K that yield the highest output. This can be done by taking partial derivatives of the production function with respect to L and K, and setting them equal to zero to find the critical points. Then, we can evaluate the second partial derivatives to determine if these points are local maximums or minimums. The corresponding level of production can be obtained by substituting the values of L and K into the production function.