Question

A merchant buys a certain item for Rs. 200 per case and sells it for Rs.500 per case. The high mark-upreflects the brittleness of the item and the great risk in stocking it. Any unsold items must be scrappedat the end of the day and have no salvage value. The merchant wants to know how many units of theitem should be stocked at the beginning of the day. The past hundred days' sales are tabulated here:

Daily sales (No. of cases) 12 13 14 15
No. of days 15 20 40 25

Answer 1

Given : A merchant buys a certain item for Rs. 200 per case and sells it for Rs.500 per case . Any unsold items must be scrapped at the end of the day and have no salvage value.The past hundred days' sales is given

To find :  how many units of the item should be stocked at the beginning of the day. T

Solution:

Daily sales (No. of cases) 12   13   14   15

No. of days                        15   20  40  25

Lets check profit  for each case  of unit stocked 12 , 13 , 14 , or 15

Profit = number of units sold (or units in stocks) which ever is less * 500 - 200 * number of items in stocks

                                     

Daily Sells       Profit  based on 12 item is stocks     Days   Profit

12                    12* 500 - 12* 200 = 3600                    15       54000

13                    12* 500 - 12* 200 = 3600                    20       72000

14                     12* 500 - 12* 200 = 3600                   40      144000          

15                     12* 500 - 12* 200 = 3600                   25         90000

                                                                   Total                    360000

Daily Sells       Profit  based on 13 item is stocks     Days   Profit

12                    12* 500 - 13* 200 = 3400                   15       51000

13                    13* 500 - 13* 200 = 3900                   20       78000

14                    13* 500 - 13* 200 = 3900                   40      156000          

15                    13* 500 - 13* 200 = 3900                   25        97500

                                                                   Total                    382500

Daily Sells       Profit  based on 14 item is stocks     Days   Profit

12                    12* 500 - 14* 200 = 3200                   15       48000

13                    13* 500 - 14* 200 = 3700                   20       74000

14                    14* 500 - 14* 200 = 4200                   40      168000          

15                    14* 500 - 14* 200 = 4200                   25       105000

                                                                   Total                    395000

Daily Sells       Profit  based on 15 item is stocks     Days   Profit

12                    12* 500 - 15* 200 = 3000                   15       45000

13                    13* 500 - 15* 200 = 3500                   20       70000

14                    14* 500 - 15* 200 = 4000                   40      160000          

15                    15* 500 - 15* 200 = 4500                   25       112500

                                                                   Total                    387500

   395000 is the maximum profit when 14 items are in stock

14 units should be stocked  

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