SOLUTION: P(x) = -.2x^2 +300x-200. What is the profit if 500 are sold? What value of x will the profit be at a maximum?

Algebra ->  Functions -> SOLUTION: P(x) = -.2x^2 +300x-200. What is the profit if 500 are sold? What value of x will the profit be at a maximum?      Log On


   

Question 97347: P(x) = -.2x^2 +300x-200. What is the profit if 500 are sold? What value of x will the profit be at a maximum?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
p%28x%29=-.2x%5E2%2B300x-200 Start with the given polynomial


p%28500%29=-.2%28500%29%5E2%2B300%28500%29-200 Plug in x=500


p%28500%29=-.2%28250000%29%2B300%28500%29-200 Evaluate %28500%29%5E2 to get 250,000


p%28500%29=-50000%2B300%28500%29-200 Multiply -.2 and 250,000 to get -50,000

p%28500%29=-50000%2B150000-200 Multiply 300 and 500 to get 150,000


p%28500%29=99800 Combine like terms


So when 500 are sold, the profit is $99,800



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To find the maximum x-value, you simply need to find the axis of symmetry. So the axis of symmetry is:


x=-b%2F2a where b is the x-coefficient and a is the x%5E2 coefficient


x=-300%2F2%28-.2%29 Plug in a=-.2 and b=300


x=-300%2F-0.4 Multiply


x=750 Divide


So when 750 are sold, the profit is at the maximum