A 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. Determine the total product function (TPL) for input L.
b. Determine the marginal product function for input L.
c. Determine the average product function for input L.
d. Find the number of units of input L that maximizes the total product function.
e. Find the number of units of input L that maximizes the marginal product function.
f. Find the number of units of input L that maximizes the average product function.