SOLUTION: If 100 pear trees are planted, then the annual revenue is $90 per tree. If more trees are planted, the annual revenue per tree will be reduced by $.50 for each additional tree plan

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If 100 pear trees are planted, then the annual revenue is $90 per tree. If more trees are planted, the annual revenue per tree will be reduced by $.50 for each additional tree plan      Log On


   



Question 1149687: If 100 pear trees are planted, then the annual revenue is $90 per tree. If more trees are planted, the annual revenue per tree will be reduced by $.50 for each additional tree planted. How many trees should be planted to maximize the revenue from the orchard for one year.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R+ = the revenue per year
Let +n+ = the number of trees planted per year ( n is greater than 100 )
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+R+=+90%2A100+%2B+%28+n+-+100+%29%2A%28+90+-+.5n+%29+
+R+=+9000+%2B+%28+90n+-+.5n%5E2+-+9000+%2B+50n+%29+
+R+=+9000+%2B+90n+-+.5n%5E2+-+9000+%2B+50n+
+R+=+-.5n%5E2+%2B140n++
The maximum +n+ is at:
+n%5Bmax%5D+=+%28-140%29%2F%282%2A%28-.5%29%29+
+n%5Bmax%5D+=+140+ trees
Plug this value back into equation
+R%5Bmax%5D+=-+.5%2A140%5E2+%2B+140%2A140++
+R%5Bmax%5D+=+9800++
+R%5Bmax%5D+=+9800+
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Here's the plot:
+graph%28+400%2C+400%2C+-50%2C+300%2C+-1000%2C+12000%2C+-.5x%5E2+%2B+140x+%29+
Looks good, I think
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check:
Check the points where +R+=+0+
+R+=+-.5n%5E2+%2B140n++
+0+=+-.5n%5E2+%2B140n++
+n%2A%28+-.5n+%2B+140+%29+=+0+
+.5n+=+140+
+n+=+280+
This look good from plot