The profit P ( in dollars) for a manufacturer of sound systems is given by the quadratic function P(X)=-0.0003X2+150X-375000 where X is the number of units produced. What production level will yield a maximum profit?
X = -B/2A = -150/-0.0006 = 25,000 Units.
To find the production level that will yield a maximum profit, we can use the concept of vertex of a quadratic function. The vertex of a quadratic function represents its maximum or minimum point.
The quadratic function in question is: P(X) = -0.0003X^2 + 150X - 375000
The general form of a quadratic function is: f(X) = aX^2 + bX + c
Comparing the given function to the general form, we have:
a = -0.0003
b = 150
c = -375000
The x-coordinate of the vertex of a quadratic function can be found using the formula: x = -b / (2a)
Replacing the values we have: x = -150 / (2 * -0.0003)
Calculating further: x = 250000
Therefore, the production level that will yield a maximum profit is 250,000 units.