The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny.
A) $834.16
B) $420.34
C) $1,791.90
D) $617.90
E) $1,421.16

Question

The demand function for a certain product is given by  , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny. ​
A) $834.16 
B) $420.34 
C) $1,791.90 
D) $617.90 
E) $1,421.16

Quizplus · Accepted Answer

To find the average price as demand ranges from 35 to 81 units, we need to calculate the total revenue and divide it by the total number of units sold within the given demand range.

Total revenue can be calculated by multiplying the price and quantity demanded:

Total revenue = p*q

Integrating the demand function within the given demand range, we get:

Total revenue = ∫35^81 (10000/√q) dq

= 20000(81^(1/2) - 35^(1/2))

= 20000(9 - 5.916)

= 62680

The total number of units sold within the given demand range is:

Total units sold = 81 - 35 = 46

Therefore, the average price is:

Average price = Total revenue / Total units sold

= 62680 / 46

= $1362.61

Rounding to the nearest penny, we get:

Average price = $1362.60

Thus, the best choice is D.

The Demand Function for a Certain Product Is Given by