A company sells X units of a product whose profits function is given by the quadratic model P(X) =60X-X^2 = X(60-X)
A) How many units should the company sell in order to maximize their profits
B) What will be the maximum profit if the # of units found in part (A) were sold
C) what is the maximum number of units the business can sell and still make a pofit
Once again i am stopped by quadratic functions please help me
The standard form of a quadratic function is:
a is the coefficient of and b is the coefficient of x.
Your function was
If you rearrange your function into standard form, it would look like this:
, where a = -1, b = 60.
This is the graph of a parabola that opens downward. The vertex would be the maximum point on the parabola. The x-coordinate of the vertex is given by the formula:
This formula is derived by finding the x-intercepts and dividing by 2, but that's another story. Just remember this formula.
Substituting the coefficients into that formula, I found the x-coordinate to be 30.
Substituting P(30) into , I found the y-coordinate of the vertex, which is the maximum value (profit) when 30 units are sold. P(30) = 900.