Given the Production Function Q = 72X + 15X2 – X3, where Q = Output an

Given the Production Function Q = 72X + 15X2 – X3, where Q = Output and X = Input

a. What is the Marginal Product (MP) when X = 8?
b. What is the Average Product (AP) when X = 6?
c. At what value of X will Q be at its maximum?
d. At what value of X will Diminishing Returns set in?

ANSWER

a. MP = 72 + 30X – 2X2, MP =120 when X=8;
b. AP = 72 + 15X – X2, AP=126 when X=6;
c. Q at a maximum when MP is 0, or X =12 [-2 has no meaning;]
d. Diminishing returns sets in when MP at a maximum value, or X = 5.