<DIV>11.[2.6#39] The output at a certain plant is Q= 0.08x<SUP>2</SUP> +0.12xy+0

Question

<DIV>11.[2.6#39] The output at a certain plant is Q= 0.08x<SUP>2</SUP> +0.12xy+0.03y<SUP>2</SUP> units per day, where x is the number of hours of skilled labor and y is 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 chnage in unskilled labor that should be made to offset a 1-hour increase in skilled labor to maintain output at the current level.</DIV>

Explanation / Answer

If Q= 0.08X^2 +0.12xy +0.03y^2 dq/dx= 0.16x +.0.12y dq/dy= 0.12x +0.06y At (80,200) dq/dx= 12.8+24= 36.8 dq/dy= 9.6 + 12= 21.6 This means that for 1 hour decrease in unskilled labor output will decrease by 21.6 units, and for every hour increase in skilled output will increase by 36.8 units.

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