Solution:
Given that the unit cost of manufacturing airplane engines in an aircraft factory is expressed by the function:

To evaluate the number of engines to be made so as to minimize the unit cost,
step 1: Take the derivative of C(x) with respect to x.

step 2: Evaluate the critical or stationary point of the C(x) function.
At, the stationary point, the derivative of C(x) equals zero.
Thus, at the critical point,

step 3: Take the second derivative of the C(x) function to determine the extreme points of the C(x) function.


Since the second derivative of C(x) is evaluated to be greater than zero, this implies that we have a minimum point or value of C(x).
Thus, for C(x) to be a minimum, we have the value of x to be 80.
Hence, number of engines to be made so as to minimize the unit cost is
