Question 33152
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.