The average cost per item to produce q items is given by a(q) = q^2 - 60q + 1300, for q > 0. What is the total cost C(q) of producing q goods? What is the quantity q that minimizes the marginal cost? At what production level is the average cost a minimum? What is the lowest average cost? What is the marginal cost at q = 30? How does this relate to your answer from c?
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Step 1: The total cost C(q) of producing q goods is given by the equation C(q) = q^3 - 30q^2 + 1300q. Show more…
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The average cost per item to produce $q$ items is given by $$ a(q)=0.01 q^{2}-0.6 q+13, \text { for } q>0 $$ (a) What is the total cost, $C(q)$, of producing $q$ goods? (b) What is the minimum marginal cost? What is the practical interpretation of this result? (c) At what production level is the average cost a minimum? What is the lowest average cost? (d) Compute the marginal cost at $q=30 .$ How does this relate to your answer to part (c)? Explain this relationship both analytically and in words.
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Using the Derivative
Applications to Marginality
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