The daily production costs P (in dollars) for a manufacturer of sound systems is given by the quadratic function.
P(x)= -0.003x^2+150x-375,000
Where x is the number of units produced. What production level will yield a maximum profit?
as with all parabolas, the vertex (in this case a maximum) is at
p = -b/2a = 150/.006
To find the production level that will yield a maximum profit, we need to determine the value of x that corresponds to the vertex of the quadratic function P(x).
The vertex of a quadratic function in the form of P(x) = ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, the quadratic function is P(x) = -0.003x^2 + 150x - 375,000. Comparing it to the standard form, we can see that a = -0.003, b = 150, and c = -375,000.
Using the formula, we can calculate the value of x:
x = -b / (2a)
= -150 / (2 * -0.003)
= -150 / (-0.006)
= 25,000
Therefore, a production level of 25,000 units will yield the maximum profit.