# Math Help - Cost of producing X units.....

1. ## 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?
$dc/dt = -55dx/dt + 8dx/dt$

2. 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?
$dc/dt = -55dx/dt + 8dx/dt$
you have differentiated wrong
$dc/dt = -55dx/dt + 8xdx/dt$
you have dx/dt=5
and x=8units per week...hence you can find dc/dt.

3. ?
Originally Posted by malaygoel
you have differentiated wrong
$dc/dt = -55dx/dt + 8xdx/dt$
you have dx/dt=5
and x=8units per week...hence you can find dc/dt.

4. 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?
$dc/dt = -55dx/dt + 8dx/dt$
You want to find :how fast is the production cost changing...i.e. $\frac{dc}{dt}$

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

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

$dc/dt = 45$