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

Plug in values:
\[P = 20x^{0.6}y^{0.4}\]
\[900 = 20(120)^{0.6}y^{0.4}\]
\[\frac{ 900 }{ 20(120)^{0.6} } = y^{0.4}\]
\[y = (\frac{ 900 }{ 20(120)^{0.6} })^{2.5}\]

Then find y', the derivative of f(x)