SOLUTION: A company has determined that the profit, in dollars, it can expect from the manufacture and sale of x tennis racquets is given by P = −0.01x2 + 170x − 180,000. How many racq

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Question 1207286: A company has determined that the profit, in dollars, it can expect from the manufacture and sale of x tennis racquets is given by
P = −0.01x2 + 170x − 180,000.
How many racquets should the company manufacture and sell to earn a profit of $474,900?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

P+=+-0.01x%5E2+%2B+170x+-+180000
How many racquets should the company manufacture and sell to earn a profit of $474900?

P=474900
474900+=+-0.01x%5E2+%2B+170x+-+180000
0.01x%5E2+-+170x+%2B+180000%2B474900+=0
0.01x%5E2+-+170x+%2B+654900+=0

using quadratic formula we have

x=%28-%28-170%29%2B-sqrt%28%28-170%29%5E2-4%2A0.01%2A654900%29%29%2F%282%2A0.01%29
x=%28170%2B-sqrt%2828900-26196%29%29%2F0.02
x=%28170%2B-sqrt%282704%29%29%2F0.02
x=%28170%2B-52%29%2F0.02

solutions:
x=%28170%2B52%29%2F0.02=11100
or
x=%28170-52%29%2F0.02=5900
the company manufacture should sell 5900 or 11100 racquets to earn a profit of $474900