right now:
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
My answer is correct.
A company offers the following schedule of charges: $30 per thousand for orders of 50,000 or less with the charge per thousand decreased by 37.5 cents for each thousand above 50,000. Find the order which will make the company's receipts a maximum?
How do you solve it?
2 answers
what is the final answer?