Homework SourseUsing x hours of skilled labor and y hours of unskilled labo
Using x hours of skilled labor and y hours of unskilled labor, a manufacturer can produce Q(x,y)=40xy^(1/5) units each week. Currently 40 hours of skilled labor and 243 hours of unskilled labor are being used. Suppose the manufacturer reduces the skilled labor level by 3 hours and increases the unskilled labor by 3. Use calculus to determine the approximate effect of these changes on production.
Production changes by approximately: _______________ units?
Production changes by approximately: _______________ units?
Solution
Q = (dQ/dx)x + (dQ/dy)y =
40y1/5 * (-3) + 8xy-4/5 * 3 =
-40*3*3 + 8*40*(3-4)*3 =
-360 + 320/27 =
-348.15
So the production reduces by approximately 348.15 units.
