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)= 10xy^(1/5) units each week. Currently 30 hours of skilled labor and 243 hours of unskilled labor are being used. Suppose the manufacturer reduces the skilled labor level by 4 hours and increases the unskilled labor by 3. Use calculus to determine the approximate effect of these changes on production.
Production changes by approximately?
Production changes by approximately?
Solution
Qx=10y^(1/5) Qy=10x*1/5 *y^(-4/5) Qxy=Qyx=2*y^(-1/5) dx=-4 dy=3 dq=Qxy*dx*dy(at x=30 and y= 243) =2*243^(-0.2) * (-4)*3 dq=-8 => production decreases by 8 units
