The price p (in dollars) and demand x for wireless headphones are related by x = 7,000 - 0.15 p^2. The current price of $110 is decreasing at a rate $5 per week. Find the associated revenue function R (p) and the rate of change (in dollars per week) of revenue.

Question

Mathematics

Cayden Cervantes

8 August, 12:21

The price p (in dollars) and demand x for wireless headphones are related by x = 7,000 - 0.15 p^2. The current price of $110 is decreasing at a rate $5 per week. Find the associated revenue function R (p) and the rate of change (in dollars per week) of revenue.

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Makenzie Walls · Answer 1

Total Revenue Function = 7000p - 0.15 p^3

Rate of change per unit price change = 7000 - 0.45 p^2

Step-by-step explanation:

x = 7000 - 0.15 p^2 [Quantity given]

Total Revenue is the total value of receipts from sale. TR = Price X Quantity

TR Function = p. x

= p (7000 - 0.15 p^2) = 7000p - 0.15 p^3

Rate of change in revenue, due to change in price

dTR / dP = 7000 - 0.45 p^2