Chapter10.7 - Chapter 10.7 Page 569 (i) (ii) (iii) Given...

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Chapter 10.7 Page 569 (i) Given the cost ) ( x C , ) ( ' x C is the marginal cost; (ii) Profit = Revenue – Cost, ) ( ) ( ) ( x C x R x P = = ; (iii) ) ( ' x P is the marginal profit; Example 1. A company manufactures fuel tanks for automobiles. The weekly cost (in dollars) of producing x tanks is given by 2 05 . 0 90 10000 ) ( x x x C - + = . (A) Find the marginal cost; 90 1 . 0 1 . 0 90 0 )' 05 . 0 ( )' 90 ( )' 10000 ( ) ( ' 2 + - = - + = - + = x x x x x C (B) Find the marginal cost at a production level of 500 tanks per week and interpret the result; 40 90 ) 500 ( 1 . 0 ) 500 ( ' = + - = C At the production level of 500 tanks per week, the total cost is increasing at the rate of $40 per tank. (C) Find the exact cost for the producing the 501 st tank; 95 . 39 42500 95 . 42539 ] ) 500 ( 05 . 0 ) 500 ( 90 10000 [ ] ) 501 ( 05 . 0 ) 501 ( 90 10000 [ ) 500 ( ) 501 ( 2 2 = - = - + - - + = - C C So the exact cost is $39.95. Page 570
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Chapter10.7 - Chapter 10.7 Page 569 (i) (ii) (iii) Given...

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