Business Analysis Lab Help

Hey guys, I have a question about a lab I'm doing. I'm getting two positive answers at the end and I'm not sure why. Here's the question:

Cost equations for manufacturing companies are often quadratic in nature. The ACME Widget's cost function for manufacturing widgets is C(x) = x^2 - 10x + 31, where C(x) is the cost of manufacturing x units per week (both in thousands). Find the output for a weekly cost of $15 thousand.

Here's what I have so far:

C(x) = 0 = x^2 - 10x + 16

Did the quadratic formula and got x = 2 and x = 8. Since this is a cost analysis, why am I getting two positive answers? Can someone shed some light on this and help me out a bit? Thanks in advance.

Re: Business Analysis Lab Help

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.

Re: Business Analysis Lab Help