40. Productivity Your automobile assembly plant has a Cobb-Douglas production function given by q = 10020.3 2/0.7 where q is the number of automobiles it produces per year, x is the number of employees, and y is the monthly assembly-line budget (in thousands of dollars). Annual operating costs amount to an average of $60 thousand per employee plus the operating budget of $12y thousand. Your annual budget is $1,200,000. How many employees should you hire and what should your assembly-line budget be to maximize productivity? What is the productivity at these levels? [Hint: See Example 5.]