SOLUTION: Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be so

Question 57211This question is from textbook
: Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be sold to maximize the profit? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be sold to maximize the profit?
:
p(x) = y
:
This is a quadratic equation, the value of x for a max of y is the vertex, which can be easily found using the vertex formula: x = -b/(2a)
:
In the equation y = -2x^2 + 280x - 1000; a=-2; b=280; c=-1000
:
Using those values in the vertex equation:
x = -280/(2*-2)
x = -280/-4
x = +70 items for max profit
:
If you wish to know the actual amount of profit, substitute 70 for x in the equation: p(x) = -2(70^2) + 280(70) - 1000, you should get $9,700

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