Using 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)=80xy^(1/2) units each week. Currently 100 hours of skilled labor and 9 hours of unskilled labor are being used. Suppose the manufacturer reduces the skilled labor level by 3 hours and increases the unskilled labor by 6. Use calculus to determine the approximate effect of these changes on production.
Production changes by approximately????

Solution

Q(x,y) = 80xy^1/2 Q initial= 80*100*9^1/2= 24000 units Q final= 80*97*15^1/2= 30054 units so production changes by= 30054- 24000 =6054
Using x hours of skilled labor and y hours of unskilled labor, a manufacturer can produce Q(x,y)=80xy^(1/2) units each week. Currently 100 hours of skilled labo

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