So there is no way profit = price x quantity demanded because I have q=-60p+950 and Revenue or profit=-60p^2+950p. I then have to find out the profit made by selling things at 5.50, 10 , and 15 dollars. I was told to plug these numbers into -60p^2+950p to get the profit and determine which one gives you the most profit.

I plugged in the revenue I got from the p^2 function and subtracted a cost function I had but if I just do regular profit=revenue-cost I get two different numbers?

HELP

I am not certain what you are doing. There is a silly term called gross profit, not including costs, but that is never money in the pocket...costs always have to be subtracted. Revenue is not profit. Revenue is money taken in.

I understand your confusion. Let's break down the different components and calculations involved.

First, the equation q = -60p + 950 represents the quantity demanded as a function of the price. This equation allows you to determine the quantity sold at a given price.

Next, you have the revenue equation, which is denoted as profit in this case: -60p^2 + 950p. The equation calculates the revenue generated based on the price (p). However, it's important to note that this equation represents revenue, not profit. Profit is typically calculated by subtracting costs from revenue.

If you have a separate cost function, you should subtract it from the revenue equation to find the profit. For example, let's say your cost function is C = 200q, where C represents cost, and q is the quantity sold. To find the profit, you can use the equation: profit = revenue - cost.

Here's how you can calculate profits for selling items at different prices (p) using the revenue equation (-60p^2 + 950p) and the given cost function (C = 200q):

1. Plug in p = 5.50 into the revenue equation: profit = -60(5.50)^2 + 950(5.50).
Calculate the result.

2. Plug in p = 10 into the revenue equation: profit = -60(10)^2 + 950(10).
Calculate the result.

3. Plug in p = 15 into the revenue equation: profit = -60(15)^2 + 950(15).
Calculate the result.

Compare the profits obtained from each calculation to determine which price results in the highest profit.

Doing the calculations this way ensures that the cost is properly accounted for in the profit calculation, giving you consistent results.