# Cost of producing X units.....

• Jul 6th 2009, 07:23 PM
xterminal01
Cost of producing X units.....
A manufacturer finds that the cost of producing x units weekly is
C(x)=3000-55x+4x^2 dollars

If the production level is increasing steadily at the rate of 5 units per week. how fast are production cost changing when the production level reaches 8 units per week.
So i first took the derivative but am stuck of what to do next?
$\displaystyle dc/dt = -55dx/dt + 8dx/dt$
• Jul 6th 2009, 07:46 PM
malaygoel
Quote:

Originally Posted by xterminal01
A manufacturer finds that the cost of producing x units weekly is
C(x)=3000-55x+4x^2 dollars

If the production level is increasing steadily at the rate of 5 units per week. how fast are production cost changing when the production level reaches 8 units per week.
So i first took the derivative but am stuck of what to do next?
$\displaystyle dc/dt = -55dx/dt + 8dx/dt$

you have differentiated wrong
$\displaystyle dc/dt = -55dx/dt + 8xdx/dt$
you have dx/dt=5
and x=8units per week...hence you can find dc/dt.
• Jul 6th 2009, 07:54 PM
xterminal01
?
Quote:

Originally Posted by malaygoel
you have differentiated wrong
$\displaystyle dc/dt = -55dx/dt + 8xdx/dt$
you have dx/dt=5
and x=8units per week...hence you can find dc/dt.

• Jul 6th 2009, 08:14 PM
malaygoel
Quote:

Originally Posted by xterminal01
A manufacturer finds that the cost of producing x units weekly is
C(x)=3000-55x+4x^2 dollars

If the production level is increasing steadily at the rate of 5 units per week. how fast are production cost changing when the production level reaches 8 units per week.
So i first took the derivative but am stuck of what to do next?
$\displaystyle dc/dt = -55dx/dt + 8dx/dt$

You want to find :how fast is the production cost changing...i.e.$\displaystyle \frac{dc}{dt}$

$\displaystyle dc/dt = -55\frac{dx}{dt} + 8x\frac{dx}{dt}$

plugging in the values:
$\displaystyle dc/dt = -55(5) + 8(8)(5)$

$\displaystyle dc/dt = 45$