A different interpretation of marginal cost Suppose a large company makes 25,000 gadgets per year in batches of x items at a time. After analyzing setup costs to produce each batch and tak- ing into account storage costs, it has been determined that the total cost C(x) of producing 25,000 gadgets in batches of x items at a time is given by C(x)=1250000+125000000x+1.5x a. Determine the marginal cost and average cost functions. Graph and interpret these functions. b. Determine the average cost and marginal cost when x=5000. c. The meaning of average cost and marginal cost here is differ- ent from earlier examples and exercises. Interpret the meaning of your answer in part (b).

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A different interpretation of marginal cost Suppose a large  company makes 25,000 gadgets per year in batches of x items at  a time. After analyzing setup costs to produce each batch and tak-  ing into account storage costs, it has been determined that the total  cost C(x) of producing 25,000 gadgets in batches of x items at a  time is given by  C(x)=1250000+125000000x+1.5x  a. Determine the marginal cost and average cost functions. Graph  and interpret these functions.  b. Determine the average cost and marginal cost when x=5000.  c. The meaning of average cost and marginal cost here is differ-  ent from earlier examples and exercises. Interpret the meaning  of your answer in part (b).

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Step 1  C(x)=1250000+125000000x+1.5x  Formula:  Marginal Cosr C―(x)=C(x)x  Average Cost C―′(x)=ddxC―(x)  Step 2  Marginal cost is C―(x)=1250000x+125000000x2+1.5  Average cost is: C―′(x)=ddx{(1250000x+125000000x2+1.5})  C―′(x){(−1250000x2−250000000x3})  The graph of the marginal(in blue) and average(in black) is    As the number of items increases, the marginal function decreases  As the number of items increases, the average function increases  Step 3  C―(5000)=12500005000+12500000050002+1.5  C―(5000)=256.5  C―′(5000)={(−125000050002−25000000050003})  C―(5000)=−0.052  when the number of items is 5000, the marginal cost is 256.5 and the average cost is -0.052

A different interpretation of marginal cost Suppose a large company makes 25,00

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