The output of a certain plant is Q = 0.09X2 + 0.12xy + 0.02 y2 units per day, wh

Question

The output of a certain plant is Q = 0.09X2 + 0.12xy + 0.02 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, 90 hours of skilled labor and 500 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

am the same one as 1st one : after correcting

dQ = 0.18xdx + 0.12(xdy+ydx) + 0.04ydy

x = 90 ; y = 500 ; dx=1 ; dQ = 0

i.e; 0 = 0.18*90*1 + 0.12(90dy+500*1) + 0.04*500*dy

=> 0 = 16.2 + 10.8dy + 60 + 20 dy

=> 30.8 dy = -76.2

=> dy = -76.2/30.8 = -2.474

delta y = -2.474 hours

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