If the cost of producing one item is $558, find the cost of producing 100 items. A company estimates that the marginal cost (in dollars per item) of producing x items is 1.89 − 0.002x. If the cost of producing one item is $558, find the cost of producing 100 items. (Round your answer to two decimal places.)

Expert Answers

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`c(x) = 1.89x - 0.002x^2/2 + C = 1.89x - 0.001x^2 + C`

`c(1) = 558 = 1.89(1) - 0.001(1)^2 + C` so `C = 558 - 1.89 + 0.001 = 556.111`

`c(100) = 1.89(100) - 0.001(100)^2 + 556.111 = 189 - 10 + 556.111 = 735.11`

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