Thread: Need help with a related rates word problem.

1. Need help with a related rates word problem.

The output at a certain plant is Q=.08x^2+.12xy+.03y^2 units per day, where x is the umber of hours of skilled labor used and y the number of hours of unskilled labor used. Currently, 80 hours of skilled labor and 200 hours of unskilled labor are used each day. Use calculus to estimate the change in unskilled labor that should be made to offset a 1-hour increase in skilled labor so that output will be maintained at its current level.

The answer in the book says that delta y = -1.704

This is what I have done, no idea if it is right of wrong:
.08(80)^2+12(80)(200)+.03(200)^2=3632
I then changed 80 to 81
.08(81)^2+12(81)(y)+.03(y)^2=3632
534.88+972y+.03y^2=3632
972y+.03y^2=3107.12

I have no idea where to go from there. Any help is greatly appreciated :3

2. Re: Need help with a related rates word problem.

You're not really answering the question are you ? It says that you are to use calculus.

The formula that you should be using is

$\displaystyle \delta Q \approx \frac{\partial Q}{\partial x}\delta x + \frac{\partial Q}{\partial y}\delta y.$

Calculate the partial derivatives and substitute in the given values for $\displaystyle x,$ $\displaystyle y,$ $\displaystyle \delta x,$ $\displaystyle \delta Q,$ and then solve the resulting equation for the unknown $\displaystyle \delta y.$