Certain production process employs two inputs--labor (L) and raw materials (R). Output (Q) is a function of these two inputs and is given by the following relationship:
Q = 6L2 R2- 0.10L3 R3
Assume that raw materials (input R) are fixed at 10 units.
a) Find the number of units of input L that maximizes the total product function.
b) Find the number of units of input L that maximizes the marginal product function.
c) Find the number of units of input L that maximizes the average product function.
d) Determine the boundaries for the three stages of production.