The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 digital camera is as follows.
P(x) = -0.06 x^2 + 480 x - 110,000
To maximize its profits, how many cameras should Cannon produce each month?
recall that the vertex of a parabola is at x = -b/2a = 480/0.12 = ?
To maximize profits, we need to find the maximum value of the profit function P(x) = -0.06x^2 + 480x - 110,000.
To find the maximum, we need to determine the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -0.06 and b = 480.
x = -480 / (2 * -0.06)
x = -480 / -0.12
x = 4,000
Therefore, Cannon should produce 4,000 cameras each month to maximize its profits.
To find the number of cameras Cannon Precision Instruments should produce each month to maximize its profits, we need to determine the value of x that corresponds to the vertex of the quadratic function P(x) = -0.06x^2 + 480x - 110,000.
The vertex of a quadratic function is given by the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic function in the form ax^2 + bx + c.
In this case, a = -0.06, b = 480, and c = -110,000.
Using the formula x = -b / (2a), we can substitute the values:
x = -(480) / (2 * (-0.06))
x = -480 / (-0.12)
x = 4000
Thus, Cannon Precision Instruments should produce 4000 cameras each month to maximize its profits.