You can now sell 30 cars per month at $15,000 per car, and demand is increasing at a rate of 2 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.]

Step-by-step explanation:

R = P * Q

Let's make differentiation for time (t)

dR/dt = (dP/dt) * Q + P * (dQ/dt)

dR/dt = (dP/dt) * 30 + 15,000*2

The revenue starts to drop means dR/dt < 0

Then:

(dP/dt) * 30 + 15,000*2 < 0

(dP/dt) * 30 < - 30,000

dP/dt < - 1,000

Thus, the monthly revenue starts to drop when the price drops more than $1,000 per month.