SOLUTION: The total coast for a company to manufacture and sell x items per week is C= 60x +300, whereas the revenue brought in by selling all x items is R= 100x - .5x^2. How many items must

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Question 707446: The total coast for a company to manufacture and sell x items per week is C= 60x +300, whereas the revenue brought in by selling all x items is R= 100x - .5x^2. How many items must be sold to obtain a weekly profit of $300?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The profit is Revenue minus Cost, or +P+=+R+-+C+
+R+=+100x+-+.5x%5E2+
+C+=+60x+%2B+300+
+R+-+C+=+100x+-+.5x%5E2+-+60x+-+300+
+P+=+100x+-+.5x%5E2+-+60x+-+300+
Given:
+P+=+300+
+300+=+100x+-+.5x%5E2+-+60x+-+300+
+-.5x%5E2+%2B+100x+-+60x+-+600+=+0+
+-.5x%5E2+%2B+40x+-+600+=+0+
+-x%5E2+%2B+80x+-+1200+=+0+
use quadratic formula
x+=+%28-80+%2B-+sqrt%28+80%5E2-+4%2A%28-1%29%2A%28-1200%29+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-80+%2B-+sqrt%28+6400+-+4800+%29%29%2F%28-2%29+
x+=+%28-80+%2B-+sqrt%28+1600+%29%29%2F%28-2%29+
+x+=+%28+-80+%2B+40+%29+%2F+%28-2%29+
+x+=+-40%2F+%28-2%29+
+x+=+20+
and
+x+=+%28+-80+-+40+%29+%2F+%28-2%29+
+x+=+60+
-----------
According to answers they make a profit of $300/wk
if they sell 20 items or 60 items
check answers:
+P+=+100x+-+.5x%5E2+-+60x+-+300+
+300+=+100x+-+.5x%5E2+-+60x+-+300+
+300+=+100%2A20+-+.5%2A20%5E2+-+60%2A20+-+300+
+300+=+2000+-+200+-+1200+-+300+
+300+=+2000+-+1700+
+300+=+300+
OK
and
+300+=+100%2A60+-+.5%2A60%5E2+-+60%2A60+-+300+
+300+=+6000+-+1800+-+3600+-+300+
+300+=+6000+-+5700+
+300+=+300+
OK