1. A company charges orders as follows o Orders of 50,000 items or less are char
ID: 2895273 • Letter: 1
Question
1. A company charges orders as follows o Orders of 50,000 items or less are charged at $30 per thousand. o For orders above 50,000, the charge per thousand is reduced by 373f for each thousand above 50,000. (This reduced charge per thousand is applied to the complete order.) Plot the receipts of this company versus order size and analyze the graph for all features. What order size maximizes the receipts of the company? Give the reasons why the financial management of this company is clearly incompetent.1 [1. Maximum and Minimum Values]Explanation / Answer
solution:
cost per thousand = 30
orders = 50 000
for every increase of 1000 orders, cost decreases by .375
net the number of 1000 increases be n
cost per thousand = 30 - .275n
orders = 50,000 + 1000n
receipts = (30-.375n)(50000 + 1000n)
= 1,500,000 + 30,000n - 18750n - 375n^2
= -375n^2 + 11250n +1500000
d(receipts)/dn = -750n + 11250
= 0 for a max of receipts
750n = 11250
n = 15
for a max recepts
number should be 50000+1000(15) = 65000
cost per thousand = 30 - .375(15) = $24.375
testing:
for the above answer :
receipts = 65000(24.375) = 1, 584,375
take n = 14
number = 64000
cost = 30-.375(14) = $24.75
receipts = 64000(24.75) = 1, 584,000 , ahh a bit less
take n = 16
number = 66000
cost = 30-.375(16) = $24
receipts = 66000(14) = 1,584,000 , again a bit less
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