Question

You can now sell 70 cars per month at $35,000 per car, and demand is increasing at a rate of 4 cars per month each month. What is the fastest you could drop your price before your monthly revenue starts to drop? HINT [Revenue = Price × Quantity.] dp dt = $ per month

Answer 1

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 =  70 cars

Price of each car, P = $35,000

Rate of increase in demand, $\frac{dQ}{dt}$ = 4 cars per month

Now,

Revenue, R = Price(P) × Quantity (Q)

Thus,

When monthly revenue starts to drop i.e $\frac{dR}{dt}$ < 0

⇒ $\frac{dR}{dt}$ = $\frac{d(PQ)}{dt}$ < 0

or

⇒ $P\frac{dP}{dt}+Q\frac{dQ}{dt}$ < 0

or

⇒ $70\times\frac{dP}{dt}+35,000\times4$ < 0

or

⇒ $70\times\frac{dP}{dt}$ < - 140,000

or

$\frac{dP}{dt}$ < - 2,000

Hence,

the fastest we could drop your price before your monthly revenue starts to drop is $2,000