A company needs 300,000 items per year. It costs the company $1,440 to prepare a production run of these items and $11 to produce each item. If it also costs the company $1.50 per year for each item stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized.[Input box]___ items/run

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Description: A company needs 300,000 items per year. It costs the company $1,440 to prepare a production run of these items and $11 to produce each item. If it also costs the company $1.50 per year for each item stored, find the number of items that should be pr

It is given thatA company needs 300,000 items per year.It costs the company$1,440 to prepare a production run of these items and $11 toproduce each item.If it also costs the company $1.50 per yearfor each item stored.find the number of items that should to producedin each run so that total costs of production and storage are minimized.It is Economic Lot size Model.We know thatTotal cost of production is given by:Tx=fMx+gM+kx2,where,M=Total number of units produced=300,000f=Fixed set up cost for a production run=$1440g=Cost of producing an item=$11.k=cost of storing an item up to one year =$1.75x=Number of units in each runNow,Tx=300,000×1440x+11×300,000+1.75×x2⇒Tx=432000000x+3300000+1.75x2For minimization,find first derivative and equate to zero.T'x=-432000000x2+1.752PutT'x=0,then-432000000x2+1.752=0432000000x2=1.752⇒x2=432000000×21.75⇒x=22219.68Hence,value of x would be x=22220 or x=22219.At x=22220,T22220=43200000022220+3300000+1.75×222202=3338888.444andT22219=43200000022220+3300000+1.75×222202=3338884.4Here,T22220>T22219.So that x=22219 will give minimum production cost.Hence, 22219 number of items that should be produced in eachrun so that the total cost of production of items and storage areminimized.

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A company needs 300,000 items per year. It costs the company $1,440 to prepare a production run of these items and $11 to produce each item. If it also costs the company $1.50 per year for each i stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized. |items/run

A company needs 300,000 items per year. It costs the company $1,440 to prepare a production run of these items and $11 to produce each item. If it also costs the company $1.50 per year for each i stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized. |items/run

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A company needs 300,000 items per year. It costs the company $1,440 to prepare a production run of these items and $11 to produce each item. If it also costs the company $1.50 per year for each item stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized.

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