Suppose Ralph hires workers at his supermarket at a wage of $12/hour. Ralph currently has 10 ...

Suppose Ralph hires workers at his supermarket at a wage of $12/hour. Ralph currently has 10 checkstands (i.e., capital) with a rental rate of $10/hour. Production of customers served (i.e., output) is determined by the hourly production function
      f(L,K) = 0.5L3/4K2
For the questions that follow, the number of checkstands is fixed. Show your work clearly.
a.   If Ralph wants to serve 400 customers per hour, how many workers must he employ? How much will it cost to serve 400 customers per hour?
b.   Derive Ralph's short-run cost function with the 10 checkstands.
c.   Derive the equations for the MC, AC, AVC, and AFC.