SOLUTION: A plane with 150 seats may be chartered for$240 per person plus a fee of $6 per person for each empty seat. What number of passengers will provide the maximum income?

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Question 1155802: A plane with 150 seats may be chartered for$240 per person plus a fee of $6 per person for each empty seat. What number of passengers will provide the maximum income?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of filled seats
Let +I+ = the income
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+I+=+240n+%2B+6n%2A%28+150+-+n+%29+
This is:
[ Income ] = [ price/passenger x filled seats ] + [ cost/ empty seat x empty seats x filled seats ]
+I+=+240n+%2B+900n+-+6n%5E2+
+I+=+-6n%5E2+%2B+1140n+
The n-value of the peak is at:
+-b%2F%282a%29+=+-1140+%2F+%28+2%2A%28-6%29%29+
+-b%2F%282a%29+=+95+
95 passengers give the maximum income
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check:
The max income is:
+I+=+240n+%2B+6n%2A%28+150+-+n+%29+
+I%5Bmax%5D+=+240%2A95+%2B+6%2A95%2A%28+150+-+95+%29+
+I%5Bmax%5D+=+22800+%2B+570%2A55+
+I%5Bmax%5D+=+22800+%2B+31350+
+I%5Bmax%5D+=+54150+
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Here is the plot:
+graph%28+500%2C+500%2C+-20%2C+200%2C+-6000%2C+60000%2C+-6x%5E2+%2B+1140x+%29+
Looks like a match with my answer