Final answer:
The company should charge $30 to maximize its monthly revenue, with the maximum revenue being $2,100,000.
Step-by-step explanation:
To calculate how much the company should charge to maximize monthly revenue, let's define the variables: let x represent the number of $1 increases in the monthly subscription price. With each increase of $1, the company loses 5,000 subscribers. Therefore, the new price, P, can be represented by P = 20 + x, and the new number of subscribers, S, can be represented by S = 120,000 - 5,000x.
The monthly revenue, R, can be calculated as R = P * S or R = (20 + x)(120,000 - 5,000x). Expanding and simplifying gives us R = 2,400,000 + 100,000x - 5,000x^2. To find the revenue-maximizing number of subscribers, we need to find the vertex of this parabolic equation, which occurs at x = -b/(2a). In our equation, a = -5,000 and b = 100,000, so the vertex is at x = -100,000 / (2 * -5,000) = 10.
Now, we calculate the optimal price and revenue. The optimal price increase is $10, so the new price is P = 20 + 10 = $30. The number of subscribers after the price increase is S = 120,000 - 5,000(10) = 70,000. Therefore, the maximum monthly revenue is R = $30 * 70,000 = $2,100,000.