To determine the number of subscribers that will result in maximum revenue for the television company, we can follow these steps:
Step 1: Calculate the number of additional subscribers beyond 1000.
Let x be the number of additional subscribers beyond 1000. We can calculate it using the formula:
x = Total number of subscribers - 1000
Step 2: Calculate the discount per subscriber.
The discount per subscriber is $0.10 for every additional 10 subscribers beyond 1000. So, the discount per subscriber can be calculated as:
Discount per subscriber = (x / 10) * $0.10
Step 3: Calculate the total revenue for the television company.
The total revenue is the product of the number of subscribers and the charge per subscriber, minus the total discount given for the additional subscribers. It can be calculated as:
Total revenue = (Number of subscribers * $5) - Total discount
Step 4: Determine the number of subscribers for maximum revenue.
To find the number of subscribers that will result in maximum revenue, we need to find the value of x that maximizes the total revenue. We can start by assuming x to be zero (i.e., no additional subscribers), and then gradually increase it until the revenue starts decreasing.
Note: We assume that the total number of subscribers cannot exceed a given limit, and we aim to maximize revenue within that limit.
Let's put these steps into action to find the number of subscribers for maximum revenue.
Start with x = 0 (no additional subscribers beyond 1000).
Number of subscribers = 1000 + x
Charge per subscriber = $5
The total discount for the additional subscribers can be calculated as:
Total discount = (x / 10) * $0.10
The total revenue can be calculated as:
Total revenue = (Number of subscribers * $5) - Total discount
Increase x by 1 and recalculate the total revenue.
Repeat this process until the revenue starts decreasing.
By comparing the total revenue for different values of x, we can identify the number of subscribers that will result in maximum revenue for the television company.