Answer:
the fastest we could drop your price before your monthly revenue starts to drop is $2,000
Explanation:
Data provided in the question:
Cars sold per month, Q = Â 70 cars
Price of each car, P = $35,000
Rate of increase in demand, [tex]\frac{dQ}{dt}[/tex] = 4 cars per month
Now,
Revenue, R = Price(P) × Quantity (Q)
Thus,
When monthly revenue starts to drop i.e [tex]\frac{dR}{dt}[/tex] < 0
⇒ [tex]\frac{dR}{dt}[/tex] = [tex]\frac{d(PQ)}{dt}[/tex] < 0
or
⇒ [tex]P\frac{dP}{dt}+Q\frac{dQ}{dt}[/tex] < 0
or
⇒ [tex]70\times\frac{dP}{dt}+35,000\times4[/tex] < 0
or
⇒ [tex]70\times\frac{dP}{dt}[/tex] < - 140,000
or
[tex]\frac{dP}{dt}[/tex] < - 2,000
Hence,
the fastest we could drop your price before your monthly revenue starts to drop is $2,000
