Question

A company needs 50,000 items during a year. It costs $1000 to set up each production run and each item costs $22 to produce. It also costs $4 per year to store an item. a. 2 pts If x items are in each production run, how many production runs are needed each year? b. 4 pts What is the total cost of production if x items? c. 2 pts Using the inventory control cost model, what is the total cost of storage? d. 8 pts Using the inventory control cost model, find the number of items in each production run that will minimize the total cost for the company. Be sure to show that the value you found corresponds to the minimum cost.

Answer 1

Solution Given Total no. of items produces in a year = 50,000 Cast of each production non set up = $1000 cost of each item to produce = $22 Inventory Cost for each iten = $4 lys x = No. of items produced in one production ron. Total production So, No. of production non = b) Total cost of production = (Cost of set up) (Cost to produce items) = (1000x500) +( 22 **) 5 x 10 + 22 x c) Total Cost of storage Cost of storage aux No. of items = 4 x 7 d) Total احمين Cost = 5x10 + R2 00 +420 Total Cast 5x10 4 26 x CSScanned with CamScanner

Cost, To minimize total d T bul 5*10² +26* 6) :) - 500 5x107 +26 5*107 => x2 26 X 5*10 26 - 1387 Hence, No. of items in each rona se = 1387 items And Total Cost (T) 1993 ")(2641951) =$72111.03 Take x,= 1386 T - Total Cost (T.)= $72 111.038 T then, and if take x = 1388 Total Cost (I) = $72111.05 >T Hence, Total Cost is minimum when x = 1387 itens and, TC = 872 111.03 CS Scanned with CamScanner