Explanation Given: A cell phone manufacturer produces 145,000 phones a year. It costs $ 3.25 to store each phone for one year and $230 to produce each batch. Calculation: The company has two types of costs associated with the production of its product. A cost associated with manufacturing the item and a cost associated with storing the finished product. Let the variables be defined as x is number of batches to be manufactured annually, k is cost of storing one unit of the product for one year ( $ 3.25 ) , a is fixed setup cost to manufacture the product ( $ 230 ) , b is variable cost of manufacturing a single unit of the product and M is total number of units produced annually ( 145 , 000 ) . During a year, the company will produce x batches of the phone, with M x units of the phones produced per batch. Each batch has a fixed cost a and a variable cost b per phone, so the manufacturing cost per batch is: a + b ( M x ) There are x batches per year, so the total annual manufacturing cost is: [ a + b ( M x ) ] x …...…... (1) Each batch consists of M x units, and demand is constant, therefore, it is common to assume an average inventory of 1 2 ( M x ) = M 2 x . The cost to store one unit of phone for a year is k , so the total storage cost is: k ( M 2 x ) = k M 2 x …...…... (2) The total production cost is the sum of the manufacturing and storage costs, or the sum of equations ( 1 ) and ( 2 ) . If T ( x ) is the total cost of producing x batches, T ( x ) = [ a + b ( M x ) ] x + k M 2 x = a x + b M + k M 2 x Now find the value of x that will minimize T ( x )

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ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

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Chapter 12, Problem 63RE

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To calculate: The number of batches that should be produced annually if a cell phone manufacturer produces 145,000 phones a year. It costs $3.25 to store each phone for one year and $230 to produce each batch.

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Chapter 12, Problem 62RE

Chapter 12, Problem 64RE

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The number of batches that should be produced annually if a cell phone manufacturer produces 145,000 phones a year. It costs $ 3.25 to store each phone for one year and $230 to produce each batch.

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To calculate: The number of batches that should be produced annually if a cell phone manufacturer produces 145,000 phones a year. It costs $3.25 to store each phone for one year and $230 to produce each batch.

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