Chapter 5.2, Problem 65E

Resource Allocation Your automobile assembly plant has a Cobb-Douglas production function given by

$q=x^{0.4}{y}^{0.6},$

where q is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $20,000 per employee plus the operating budget of $\$365y$. Assume that you wish to produce 1,000 automobiles per year at a minimum cost. How many employees should you hire? [HINT: See Example 5.]