Question

11. The profit (in dollars) made by a bagel shop selling x bagels is given by

a. How many bagels should be produced to maximize the profit?
b. What is the maximum profit?

Answer 1

\[P(x)=2x-\frac{ x^2 }{ 20,000? }-5000\]

Answer 2

Would really appreciate if somone could show me the whole process in detail.

Answer 3

So in order to make the most money off of the bagels, first you need to find your critical numbers. In this case you take the derivative of your equation and set it equal to zero. This will give you the critical number. At which point you need to test it to see if it is a maximum or not. If you check the intervals on either side, you should see that on one side it is still increasing (or positive) and on the other side it is starting to decrease. This would mean you are indeed maximizing the equation and making the most money. At which point depending on the assignment, you may need to check it against other possible options as well as verify that it is answering the question.

Answer 4

In other words, Set your equation in the form \[P(x) = -\frac{ x^2 }{ 20000 } + 2x -5000\] take \[P'(x)\] and set your equation equal to zero.