CHAPTER SUMMARY647Using x skilled and y anskilled workers, a manufacturer can produce Q(x, y) = 60x^1/3y^2/3 units per day.Currently the manufacturer employs 10 skilledworkers and 40 unskilled workers and is planningto hire 1 additional skilled worker. Use calculus toestimate the corresponding change that themanufacturer should make in the level of unskilledlabor so that the total output will remain theER SUMMARYsame.

Answer:The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.Step-by-step explanation:Q(x,y) = 60 x^⅓ y^⅔Take the partial derivatives with respect to x and y.∂Q/∂x = 20 x^-⅔ y^⅔∂Q/∂y = 40 x^⅓ y^-⅓So the total differential is:dQ = ∂Q/∂x dx + ∂Q/∂y dydQ = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dyIf dQ = 0:0 = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dyIf x = 10, y = 40, and dx = 1:0 = 20 (10)^-⅔ (40)^⅔ (1) + 40 (10)^⅓ (40)^-⅓ dy0 = 20 (4)^⅔ + 40 (1/4)^⅓ dy-20 (4)^⅔ = 40 (1/4)^⅓ dy-20 (4)^⅔ (1/4)^⅔ = 40 (1/4)^⅓ (1/4)^⅔ dy-20 = 40 (1/4) dy-20 = 10 dydy = -2The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.