Final answer:
To find the minimum unit cost for the manufacturing of copy machines, we utilize the vertex formula for a quadratic function. Calculating -b/(2a), we determine the x-value to be 230, which when plugged back into the cost function, reveals that none of the options A, B, C, or D are correct.
Step-by-step explanation:
The question asks about finding the minimum unit cost for manufacturing copy machines, given a quadratic function of cost in terms of the number of machines made, C(x) = 0.9x^2 - 414x + 65,441. We recognize this as a parabolic function that opens upwards, since the coefficient of x^2 is positive, suggesting the vertex of the parabola will provide the minimum value.
To find the minimum cost, we need to locate the vertex of the parabola, which occurs at the x-value -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x, derived from the standard form of a quadratic equation, ax^2 + bx + c. In the given function, a is 0.9 and b is -414, therefore:
x = -(-414) / (2 * 0.9)
x = 414 / 1.8
x = 230
Plug this x value into the cost function to find the minimum cost:
C(230) = 0.9(230)^2 - 414(230) + 65,441
Hence, the correct answer is neither A, B, C, nor D, as they do not match the calculated x-value of 230 for the minimum unit cost.