Lesson 9-filled

Lesson 9-filled - Math 1314 Lesson 9 Marginal Functions in...

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Math 1314 Lesson 9 Marginal Functions in Economics Marginal Cost Suppose a business owner is operating a plant that manufactures a certain product at a known level. Sometimes the business owner will want to know how much it costs to produce one more unit of this product. The cost of producing this additional item is called the marginal cost . Example 1 : Suppose the total cost in dollars per week by ABC Corporation for producing its best-selling product is given by . 4 . 0 3000 000 , 10 ) ( 2 x x x C - + = Find the actual cost of producing the 101 st item. The cost of producing the 101 st item can be found by computing the average rate of change, that is by computing 100 101 ) 100 ( ) 101 ( - - C C . Note that x h x x C h x C C C - + - + = - - ) ( ) ( ) ( 100 101 ) 100 ( ) 101 ( where x = 100 and h = 1.
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The right hand side of this equation is the formula for average rate of change of the cost function. This will give us the actual cost of producing the next item. However, it is often inconvenient to use. For this reason, marginal cost is usually approximated by the instantaneous rate of change of the total cost function evaluated at the specific point of interest. That is to say, we’ll find the derivative and substitute in our point of interest. Example 2
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Lesson 9-filled - Math 1314 Lesson 9 Marginal Functions in...

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