Question

he number of retro portable CD players you are prepared to supply to a retail outlet every week is given by the formula q = 0.1p2 + 9p where p is the price it offers you. The retail outlet is currently offering you $100 per CD player. If the price it offers decreases at a rate of $1 per week, how will this affect the number you supply? The supply will at a rate of CD players per week.

Answer 1

Answer:

Supply will decrease at the rate of 29 CDs per week.

Step-by-step explanation:

The number of retro portable CD players prepared to supply to a retail outlet every week is represented by the formula

q = 0.1p²  + 9p

Here p = price offered

price it offers decreases at a rate of $1 per week.

In other words, $\frac{dp}{dt}=(- 1) per week$

Now we differentiate the given equation

$\frac{dq}{dt}=\frac{d}{dt}(0.1p^{2}+9p )$

$\frac{dq}{dt}=[0.1(2p)+9]\frac{dp}{dt}$

Since, $\frac{dp}{dt}=(- 1) per week$

$\frac{dq}{dt}=(-1)[0.1(2p)+9]$

For p = 100,

$\frac{dq}{dt}=(-1)[(0.1\times 200)+9]$

= (-1)[20+9]

= -29

Therefore, $\frac{dq}{dt}=(-29)$

Supply will decrease at the rate the rate of 29 CDs per week.