Popsi Inc. produces soft drinks in quantity q in a manufacturing plant in Canada with labor input L and machines K according to

the production function q = f(K, L) = 7L + (3/2)9K^1/2)(L^2) − (L^3)/3.

In the short run, no additional machinery can be used, but workers can work overtime, so that labor input is flexible. Assume that K = 9.

(a) In the short-run, how much additional output does an additional (small) unit of labor produce if initially L = 4? How much output does each of these 4 units of labor produce on average? Why does the average product of labor increase if you add a (small) unit of labor?

(b) For which value of L do the functions MPL and APL intersect? What is the maximum of the APL function (where its slope is zero)? What is the connection?