An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If
x engines are made, then the unit cost is given by the function C (x) = 0.1x^2 - 68x + 19,017. What is the minimum unit cost?
To find the minimum unit cost, we need to find the vertex of the quadratic function C(x) = 0.1x^2 - 68x + 19,017.
The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b/2a.
In this case, a = 0.1 and b = -68, so x = -(-68)/2(0.1) = 340.
To find the minimum unit cost, we substitute x = 340 into the function C(x):
C(340) = 0.1(340)^2 - 68(340) + 19,017
C(340) = 0.1(115600) - 23120 + 19,017
C(340) = 11560 - 23120 + 19,017
C(340) = 3,457
Therefore, the minimum unit cost to make each airplane engine is $3,457.