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.

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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.

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