TEXP51 Cobb-Douglas employee-robot
A certain company is manufacturing automobile parts using both employees and robots. The production formula relating employees and robots follows the Cobb-Douglas model
where n is the number of employees and r is the number of robots.
The company is presently making 1200 pieces per month with 20 employees, and is increasing the number of robots at the rate of 1 per month.
What is the situation for employees at this point?
To find a relation between n and r, insert 1200 for P, and take a time derivative. This is the only way to develop a relationship between n and r that contains a dr/dt term.
Now solve for r with the data for this situation
So there are 20 robots ands 20 employees.
Place these numbers into the equation for dn/dt and write
For the given dr/dt of -1, three employees can be replaced ny 2 robots.