SOLUTION: Doug wants to start a physical therapy practice. His financial advisor comes up with the following profit function for his business: P(x)=-1/2x^2+150x-10000 where x represents the

Question 1107129: Doug wants to start a physical therapy practice. His financial advisor comes up with the following profit function for his business: P(x)=-1/2x^2+150x-10000 where x represents the amount, in dollars, that he charges his clients. How much will it cost for him to start the business? What should he charge his clients to make the most profit?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
start up is when x=0, since he hasn't charged anything, and that is -10,000 or a cost to him of $10,000, since the function is profit.
The maximum is at the vertex of the quadratic, where x=-b/2a
-(x/2)^2+150x-10000, a=-1/2 and b=150
x=(-150)/-(1/2) or $300

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