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Section 4.5 Example problem PC Version

# Section 4.5 Example problem PC Version - Example 1 The...

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Example 1. The average cost of producing q items is given by the function . From this determine each of the following: a.The total cost equation C(q). b. The marginal cost (MC or C’) b.Find the lowest possible average cost by using the 1 st derivative of the average cost. c.Find the lowest possible average cost by finding where average cost is equal to marginal cost. a ( q ) = q 2 - 14 q + 1000 Answer nsider the “average cost equation” given on page 196, but solve it for “cost”: a ( q ) = C ( q ) q Multiplying both sides of the equation by q yields… Picture 11 Picture 12 C ( q ) = q a ( q ) C ( q ) = q a ( q ) = q q 2 - 14 q + 1000 ( 29 = q 3 - 14 q 2 + 1000 q (Hit any key or click mouse to continue)

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(Hit any key or click mouse to continue) Find the marginal cost. Remember that MC=C’ C ( q ) = q 3 - 14 q 2 + 1000 q Taking the 1 st derivative yields…. C '( q ) = 3 q 2 - 28 q + 1000 o find the minimum average cost we can take the 1 st derivative of the average cost function. a ( q ) = q 2 - 14 q + 1000 Taking the 1 st derivative yields… a '( q ) = 2 q - 14 Next we set this to 0 and solve.
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