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Business and Economics
                                The marginal cost of producing an item is the rate at which its
                                cost changes with respect to the number of items produced.
                                Thus if C(x) is the cost of producing x items, the marginal cost
                                is C (x).

                                    The marginal cost approximates the additional cost nec-
                                essary to produce one additional item. Thus C (x) is the ap-

                                proximate cost incurred to produce the (x + 1)st item.
                                    Similarly, if R(x) and P(x) represent the revenue and
                                profit, respectively, in selling a quantity of x units, then R (x)


                                represents marginal revenue and P (x) the marginal profit.
                                EXAMPLE 14
                                Suppose the total cost of producing x items is given by the
                                function
                                                           3
                                                                      2
                                             C(x) = 0.001x + 0.025x + 3x + 5
                                Compute the marginal cost of producing the 51st item.


                                    Solution
                                    Since C (x) is the approximate cost incurred to produce


                                the (x + 1)st item we need to compute C (50).
                                                             2

                                               C (x) = 0.003x + 0.05x + 3
                                                                2

                                             C (50) = 0.003(50) + 0.05(50) + 3
                                                    = 7.50 + 2.50 + 3
                                                    = $13.00

                                The marginal cost is $13.00. For comparison, the exact cost to
                                produce the 51st item is

                                                              3
                                                                           2
                                   C(51) − C(50) = [0.001(51) + 0.025(51) + 3(51) + 5]
                                                                             2
                                                                3
                                                    −[0.001(50) + 0.025(50) + 3(50) + 5]
                                                 = 355.676 − 342.50
                                                 = $13.176


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