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67. A manufacturer determines by curve-fitting methods that its marginal revenue is given by R'(1) = 1000e'/ and its marginal cost by C'() = 1000

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67. A manufacturer determines by curve-fitting methods that its marginal revenue is given by R'(1) = 1000e'/ and its marginal cost by C'() = 1000 - 21, r days after January 1. The revenue and cost are in dollars. (a) Suppose R(0) = 0, C(0) = 0. Find, by means of integration, formulas for R() and C(t). (b) The total profit is P = R - C. Find the total profit for the first seven days

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