Answer:
Explanation:
Here is a step-by-step explanation of the solution and how it leads to the maximum revenue:
Let's start with the current revenue generated by the TV cable company, which is the product of the number of subscribers and the monthly fee:
Current revenue = Number of subscribers * Monthly fee
Current revenue = 6400 * $28
Current revenue = $179,200
To increase the revenue, the TV cable company can decrease the monthly fee by $0.50, which will result in an increase in the number of subscribers by 160 for each $0.50 decrease. Let's calculate the additional revenue generated by each $0.50 decrease in the monthly fee:
Additional revenue per decrease in monthly fee = Increase in subscribers * Decrease in monthly fee
Additional revenue per decrease in monthly fee = 160 * $0.50
Additional revenue per decrease in monthly fee = $80
The TV cable company can continue to decrease the monthly fee by $0.50 until the revenue stops increasing. Let's calculate the number of $0.50 decreases in monthly fee required to reach the maximum revenue:
Number of $0.50 decreases in monthly fee = (Total revenue - Current revenue) / Additional revenue per decrease in monthly fee
Number of $0.50 decreases in monthly fee = ($20,000,000 - $179,200) / $80
Number of $0.50 decreases in monthly fee = 248,525
The corresponding decrease in monthly fee is:
Decrease in monthly fee = Number of $0.50 decreases in monthly fee * Decrease in monthly fee
Decrease in monthly fee = 248,525 * $0.50
Decrease in monthly fee = $124,262.50
The corresponding increase in subscribers is:
Increase in subscribers = Number of $0.50 decreases in monthly fee * Increase in subscribers
Increase in subscribers = 248,525 * 160
Increase in subscribers = 39,764,000
The total number of subscribers at the maximum revenue point is:
Total subscribers = 6400 + Increase in subscribers
Total subscribers = 6400 + 39,764,000
Total subscribers = 39,770,400
The monthly fee at the maximum revenue point is:
Monthly fee = Current revenue / Total subscribers
Monthly fee = $179,200 / 39,770,400
Monthly fee = $0.0045
The maximum revenue is:
Maximum revenue = Total subscribers * Monthly fee
Maximum revenue = 39,770,400 * $0.0045
Maximum revenue = $178,966.80
Therefore, the TV cable company can generate maximum revenue of $178,966.80 per month by decreasing the monthly fee by $0.50 for each 160 additional subscribers.