Question

The number of retro portable CD players you are prepared to supply to a retail outlet every week is given by the formula q = 0.2p^2 + 2p where p is the price it offers you. The retail outlet is currently offering you $70 per CD player. If the price it offers decreases at a rate of $1 per week, how will this affect the number you supply?

Answer 1

Answer:

Decreasing by 30 per week

Step-by-step explanation:

$q = 0.2p^2 + 2p$

$\frac{dq}{dt}=0.4p \frac{dp}{dt} + 2\frac{dp}{dt}$

$\frac{dq}{dt}=(0.4p + 2)\frac{dp}{dt}$

At p=70,  $\frac{dp}{dt}=-1$

$\frac{dq}{dt}=(0.4X70 + 2)(-1)$

$\frac{dq}{dt}=-30$

The number supplied is decreasing by 30 per week.