x^2-10x+16 = (x-2)(x-8) = 0, so the solutions are correct. This means that making 2 thousand units a week costs as much as 8 thousand units a week (that cost being $15 thousand).

I think part of this would have to deal with the principle of supply and demand and machine/labor costs. If we wanted to find the most efficient production target, we can take the derivative of the cost function to find its minimum

C'(x) = 2x-10 = 2(x-5). Setting C'(x) = 0, x=5 is a critical point. C(5) = 25-50+31 = 6 thousand, so making 5 thousand units a week is most cost efficient.