SOLUTION: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by: P(x) = -0.001x^

Question 33152This question is from textbook College Algebra
: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by:
P(x) = -0.001x^2 + 3x - 1800
What is his maximum profit per day, and how many cans must he sell for maximum profit?
Thank you very much! This question is from textbook College Algebra

Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
P(x) is a quadratic function representing a function for parabola.
The parabola P(x) opens downward; implying the maximum value of the function (for profit) is attained at its vertex.
The x-coordinate of the vertex is found from -b/2a (for f(x) = ax^2+bx+c);
In this example a=-.001 and b=3
Thus, x-coordinate of the vertex is 3/.002 = 1500;
P(x) for x=1500 is -.001(225*10^4) + 4500 - 1800 = -2250 + 4500 - 1800 = 450
Answer: The vendor should sell 1,500 cans of soda to make the highest profit of $450.00.
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