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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.]

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Answer:

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.

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