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The total monthly cost (in dollars) incurred by a certain guitar manufacturer in manufacturing [Math Processing Error]x units of its Professional Series guitars is given by the function [Math Processing Error]C(x)=0

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The total monthly cost (in dollars) incurred by a certain guitar manufacturer in manufacturing [Math Processing Error]x units of its Professional Series guitars is given by the function

[Math Processing Error]C(x)=0.001x2+150x+20250.

(a) Find the average cost function

(b) Determine the production level that will result in the smallest average production cost.