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

Name: A company needs 300,000 items per year. It costs the company $1,440 t
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
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.

Math

Advanced Math

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

See similar textbooks

Similar questions

Solve with MINITAB
PLEASE ANSWER THIS QUESTION WITHIN 30 MINUTES. I WIL UPVOTE
Pls help. Tks
A company uses 3 machines X,Y and Z for their production. The company repairs each machine every time in breaks down and keeps a record of the number of breakdowns and the cost of each repair. The records for 2016 and 2021 are shown below. 2016 2021 Machine Cost of each repair (Rands) 1000 Cost of each Number of Number of repair (Rands) 800 breakdowns breakdowns 10 14 Y 400 13 800 20 2000 6. 2400 8 The cost of repair of each machine is fixed throughout the year, time machine X broke down, it cost R800 to fix it. for example in 2016, every Adapt the formula for the Laspeyres Price Index to calculate the Laspeyres "Cost of repair" Index for 2021 using 2016 as the base year. A. 137.5 В. 138.1 C. 139.8 D. 140.0
A farmer has 165 acres of land suitable for cultivating crops A and B. He has enough seeds available to plant 110 acres of crop A and 115 acres of crop B. Each acre of crop A requires 18 hours of labor, and each acre of crop B requires 19 hours of labor. The farmer has at most 3420 hours of labor available. He expects to make a profit of 130 dollars per acre on crop A and 190 dollars per acre on crop B. How many acres should the farmer plant in order to maximize his profit? acres of crop A, and acres of crop B.
Use graphpad and the T calculator: While managing a band, you want to see if your band will sell more merchandise at its shows if the band lead singer take his shirt off during their performances. For the next 18 shows, the band alternates: on the first, third, fifth, etc. shows band integrates a video screen. On the second, fourth, sixth, etc. shows the singer doesnt wear it. Merch sales per concertgoer, shirt off: 6.45, 2.75, 10.02, 8.33, 7.19, 5.42, 5.03, 7.30, 4.83 Merch sales per concertgoer, shirt on: 4.84, 3.61, 7.93, 4.20, 9.17, 3.13, 7.91, 4.68, 3.37 a. on average how much more merch do concert goers purchase win the lead singer shirt is off round to the nearest cent? b. use a two sample T interval to come up with 90% confidence interval regarding the increase in merch sales with the lead singer’s shirt is off round appropriately to the penny c.The band is about to tour Canada, and the lead singer, pondering the cold climate, says that he’ll only take his shirt off if…
Please show your solution and write readable thanks.
A successful music app tracked thenumber of song downloads eachday for a month for 4 music artists,represented by lines,,, andover the course of a month. Whichline represents an artist whosedownloads remained constant overthe month?
Explain Scheduling Daily Work Times?
.
You are thinking of making your home more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs and insulating part or all of your exterior walls. Each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† Your home has 60 light fittings and 1,200 square feet of uninsulated exterior wall. You can spend no more than $1,300 and would like to save as much per year in energy costs as possible. How many compact fluorescent light bulbs and how many square feet of insulation should you purchase? Please don't give handwritten answer..thanku
In case of LSD, each row and each column should be a complet Column. Block. Row. Design