Final answer:
The minimum unit cost ^C is found by using the vertex formula -b/(2a) on the given quadratic function C(x).
Step-by-step explanation:
The student asked for the minimum unit cost, denoted as ^C, from the quadratic function C(x) = 0.6x² - 324x + 55,426. To find this, we must recognize that the minimum unit cost in a quadratic function, which is in the form of ax² + bx + c, occurs at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula -b/(2a), where a and b are the coefficients from the quadratic equation. In this case, a = 0.6 and b = -324, so we calculate x as follows:
x = -(-324) / (2 * 0.6) = 324 / 1.2 = 270
Now, to find the minimum cost ^C, we substitute x = 270 back into the original function:
^C = 0.6(270)² - 324(270) + 55,426
^C = 0.6(72900) - 87480 + 55426
^C = 43740 - 87480 + 55426
^C = 11686
Therefore, the minimum unit cost ^C of the function C(x) is 11686.