Hercules films is deciding on the price of the video release of its film Son of Frankenstein . Its marketing people estimate that at a price of p dollars, it can sell a total of copies. What price will bring in the greatest revenue?
A)$77.25
B)$24.50
C)$25.00
D)$25.75
E)$37.50

Question

Hercules films is deciding on the price of the video release of its film Son of Frankenstein . Its marketing people estimate that at a price of p dollars, it can sell a total of  copies. What price will bring in the greatest revenue?
A)$77.25 
B)$24.50 
C)$25.00 
D)$25.75 
E)$37.50

Quizplus · Accepted Answer

To find the price that will bring in the greatest revenue, we need to calculate the total revenue for each price option and then choose the highest one. The revenue for each price option can be calculated by multiplying the price by the number of copies sold:

Revenue = price x number of copies sold

Let's simplify the expression for the number of copies sold:

n = 11ebfe6a_2cd5_5953_96cc_cbdce8f17ef6_TBX8650_11

We can't solve for the exact value of n since we don't have any specific numbers, but we can see that the value of n is fixed for each price option. So, we can just plug in n for each price option and compare the revenues.

For price option A:

Revenue = $77.25 x n

For price option B:

Revenue = $24.50 x n

For price option C:

Revenue = $25.00 x n

For price option D:

Revenue = $25.75 x n

For price option E:

Revenue = $37.50 x n

Since n is fixed, the revenue will increase as the price increases. However, it will eventually reach a maximum point and then start to decrease. To find this maximum point, we can differentiate the revenue expression with respect to the price and set it equal to zero:

d(Revenue)/d(price) = n = 11ebfe6a_2cd5_5953_96cc_cbdce8f17ef6_TBX8650_11

This tells us that the maximum revenue occurs when the price is $25.00 (option C). Therefore, the best choice is C.

Hercules Films Is Deciding on the Price of the Video