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# For the given cost function C(x)=28900+400x+x^2, what is the cost at production level...

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For the given cost function C(x)=28900+400x+x^2, what is the cost at production level 1300, avg cost at this level, marginal cost and production level that will minimize avg cost.

Posted by jjmgingrich on February 20, 2013 at 1:29 AM via web and tagged with calculus, math

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The cost function is given as C(x) = 28900+400x+x^2. If 1300 items are produced the total cost is 28900+400x+1300^2 = 2238900. The average cost for the same level of production is `2238900/1300 ~~ 1722.23` .

The average cost of production is A'(x) = C(x)/x = 28900/x + 400 + x. Marginal cost of production is C'(x) = 400 + 2x. At x = 1300, an increase in production of one unit increases the total cost by 3000.

To minimize average cost solve A'(x) = 0

=> -28900/x^2 + 1 = 0

=> x^2 = 28900

=> x = 170

The average cost is lowest when the level of production is 170.

Posted by justaguide on February 20, 2013 at 5:56 AM (Answer #1)