The demand equation for rubies at Royal Ruby Retailers is q

The demand equation for rubies at Royal Ruby Retailers is q + 1/2p = 50 where q is the number of rubies RRR can sell per week at p dollars per ruby. RRR finds that the demand for its rubies is currently 10 rubies per week and is dropping at a rate of one ruby per week. How fast is the price changing? (Round your answer to the nearest cent.)

Solution

Here on differentiatng given equation with respect to t , we get

dq/dt + (1/2p) dp/dt=0

Now as it is given that dq/dt= -1

So clearly (1/2p) dp/dt =1

or dp/dt = 2p ..........(i)

Now when q=10 then

10 +1/2p= 40

or 1/2p = 40-10=30

or 2p=1/30 or p = 1/60 = 0.0167 dollars per week

so using (i)

dp/dt = 2p = 2(0.0167) = 0.033333 dollars per week

=3.33 cents per week

Answer