Explanation Given: • Marginal cost of producing x tablet computers: C ' ( x ) = 120 − 0.06 x + 0.00001 x 2 • Set-Up Cost: $ 90 , 000 • Production is set at 3000 units Key Concepts Used: Many applications are based on the following principle. The net change in a quantity s ( t ) is equal to the integral of its rate of change: s ( t 2 ) − s ( t 1 ) = ∫ s ' ( t ) ⋅ d t t 1 t 2 . Here s ( t 2 ) − s ( t 1 ) is the net change in s ( t ) over the time interval [ t 1 , t 2 ] and ∫ s ' ( t ) ⋅ d t t 1 t 2 is Integral of rate of change. If the cost function C ( x ) of a manufacturer (the dollar cost of producing x units of a particular product or commodity), then the derivative C ' ( x ) is called Marginal Cost. The cost of increasing production from a t o b is the net change C ( b ) − C ( a ) , which is equal to the integral of the marginal cost: Cost of increasing production from a t o b = ∫ C ' ( x ) ⋅ d x a b . Here in this problem, the marginal cost of producing x tablet computers is given as C ' ( x ) = 120 − 0.06 x + 0.00001 x 2 , also it is given that the set-up cost as $ 90 , 000 and the production set at 3000 units. We have to find cost of producing 3000 units and the cost of production of 200 additional units. To find cost of producing 3000 units, we have to consider the value of a as 0 and b = 3000 . To find cost of production of 200 additional units we have to substitute a = 3000 and b = 3200 . Formula Used: Cost of increasing production from a t o b = ∫ C ' ( x ) ⋅ d x a b . Calculation: Description: Cost of increasing production from a t o b = ∫ C ' ( x ) ⋅ d x a b . Step 1 : Write the equation of the marginal cost of producing x tablet computers. C ' ( x ) = 120 − 0.06 x + 0.00001 x 2 Step 2 : Write the values of a a n d b to find the production cost of 3000 units. a = 0 b = 3000 Step 3 : Substitute these values in the given equation and calculate to find cost of producing 3000 units. C o s t o f i n c r e a s i n g p r o d u c t i o n f r o m a t o b = ∫ C ' ( x ) ⋅ d x a b C o s t o f i n c r e a s i n g p r o d u c t i o n f r o m 0 t o 3000 = ∫ ( 120 − 0.06 x + 0.00001 x 2 ) ⋅ d x 0 3000 = [ 120 x − 0.06 x 2 2 + 0.00001 x 3 3 ] 0 3000 = 120 ( x ) 0 3000 − 0...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 5.6, Problem 16E

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• Cost of producing required number of units for the given data

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Chapter 5.6, Problem 15E

Chapter 5.6, Problem 17E

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Chapter 5 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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• Cost of producing required number of units for the given data

Solution Summary: The author explains that the cost of producing 3000 units is 180, 000, and the set-up cost as 90.000.

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Chapter 5 Solutions