• Dec 8th 2012, 01:47 PM
Ceidon
If the total cost (in £s) function is given by
TC = 2Q2 + 158Q - 12000

where Q is the quantity produced

(a) What Q would minimise total costs?

(b) Use your value in (a) to find the minimum value for total costs.
pound.

Please show me how to get the answer. I would be extremely grateful. Thank you.
• Dec 8th 2012, 02:08 PM
richard1234
Set the derivative to zero to find critical points

$\frac{d(TC)}{dQ} = 4Q + 158 = 0$...this only makes sense if we can produce a negative amount. If we restrict Q to non-negative numbers, then Q = 0 minimizes cost, which turns out to be negative £12000. (also doesn't make much sense).
• Dec 8th 2012, 02:15 PM
Ceidon
• Dec 8th 2012, 02:20 PM
richard1234
Quote:

Originally Posted by Ceidon

Umm, what's the derivative of $2Q^2$ with respect to Q?
• Dec 8th 2012, 02:30 PM
Ceidon
• Dec 8th 2012, 02:50 PM
Ceidon
Quote:

Originally Posted by richard1234
Umm, what's the derivative of $2Q^2$ with respect to Q?

Sorry I got the question wrong it's

TC = 2Q^2 - 158Q + 12000
• Dec 8th 2012, 03:01 PM
skeeter
please do not post the same problem twice in different forums.

http://mathhelpforum.com/calculus/20...-question.html

also, this is not a problem in differential equations.
• Dec 8th 2012, 03:39 PM
richard1234