Question

A little help with this one please? >_<
The automobile assembly plant you manage has a Cobb-Douglas production function given by:
P = 20x^0.6*y^0.4
where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). You maintain a production level of 900 automobiles per year. If you currently employ 120 workers and are hiring new workers at a rate of 15 per year, how fast is your daily operating budget changing?

Answer 1

Take derivative of the given eqn wrt t, the time in years. Then dx/dt = 15, x = 120, dP/dt = 900. Have the eqn in terms of y and dy/dt.
Then use the original eqn, P = 900, x = 120, solve for y.
Plug the value of y into the equation with only y and dy/dt