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ssusmanw
ssusmanw ssusmanw
  • 25-01-2017
  • Mathematics
Answered

The profit function for a firm making DVDs is P(x) = 88x - x2 -1200. Find the number of DVDs at which maximum profit is achieved, and find the maximum profit. Explain your work.

Verified Answer :

bcalle
bcalle bcalle
  • 25-01-2017

This is a quadratic equation so you are looking for the vertex of the parabola.
The y value is the maximum profit.
p(x) = -x^2 + 88x - 1200
a = -1, b = 88
x = -b/2a; x = -88/(2*-1); x = 44
Plug x back in to the equation to find y.
y = -(44)^2 + 88(44) - 1200
y = 736
The number of DVD's sold were 44 for a profit of $736

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