The output of a certain plant is Q = 0.05X2 + 0.13xy + 0.03 y2 units per day, wh

Question

The output of a certain plant is Q = 0.05X2 + 0.13xy + 0.03 y2 units per day, where x is the number of hours of skilled labor used and y is the number of hours of unskilled labor used. Currently, 40 hours of skilled labor and 400 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. Round your final answer to three decimal places. delta y = hour

Explanation / Answer

Q=0.05*40^2+0.13*40*400+0.03*400^2 =5088 units per day

delta Q = 0.01x*deltax+0.13(y*deltax+x*deltay)+0.06y*deltay

delta x=1

delta Q=0

0=0.01*41*1+0.13(400*1+41*delta y)+0.06*y*deltay

-56 =29.2 delta y

delta y=-1.918 hour

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