A television company agrees to establish a community antenna in a new suburb at a charge of $5 each for 1000 subscribers or less.To encourage more subscribers,it is agreed to give a discount of $ 0.10 to each subscriber for every additional 10 subscribers in excess of 1000. for the company to receive its maximum revenue,what number of subscribers should it have?

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.

To determine the number of subscribers that would generate maximum revenue for the television company, we need to analyze the revenue generated at different subscriber levels.

Let's break down the problem step by step:

Step 1: Calculate the revenue generated from the first 1000 subscribers.
The charge per subscriber is $5, and there are 1000 subscribers or less. So the revenue for the first 1000 subscribers is 1000 * $5 = $5000.

Step 2: Determine the additional revenue generated from subscribers above 1000.
For every additional 10 subscribers, the company offers a discount of $0.10 per subscriber. This means that for every group of 10 subscribers in excess of 1000, the revenue is reduced by $0.10 per subscriber. So each group of 10 subscribers generates 10 * $0.10 = $1 less revenue compared to the charge for the first 1000 subscribers.

Step 3: Find the threshold point where the additional revenue from extra subscribers becomes less than $1 per subscriber.
To determine the subscriber level where giving the discount is no longer beneficial for generating additional revenue, we need to find the point where the reduction in revenue ($1 per group of 10 subscribers) is equal to the discount given ($0.10 per subscriber).

The reduction in revenue per group of 10 subscribers is $1, while the discount per subscriber is $0.10. So we can set up the following equation to find the threshold:

$1 = $0.10 * x
where x is the number of groups of 10 subscribers above 1000.

By solving this equation, we get:
x = $1 / ($0.10 * 10)
x = $1 / $1
x = 1 group of 10 subscribers

This means that the reduction in revenue from the discount becomes greater than $1 when we have 1 group of 10 subscribers above 1000.

Step 4: Calculate the maximum revenue.
To calculate the maximum revenue, we consider the revenue generated from the first 1000 subscribers plus the additional revenue generated from subscribers above 1000.

Maximum revenue = Revenue from first 1000 subscribers + Additional revenue from extra subscribers

The revenue from the first 1000 subscribers is $5000.

For the additional subscribers (above 1000), we have 1 group of 10 subscribers. So, the discount for this group is 10 * $0.10 = $1.

Therefore, revenue from additional subscribers = 1 * $1 = $1.

Maximum revenue = $5000 + $1 = $5001.

Therefore, the television company should aim for 1001 subscribers to maximize its revenue.