At Fenway park, they sell 5000 hot dogs at $4 per dog. They also know that for each quarter (25 cents) they raise the price, they will sell 200 less dogs. How many hot dogs should they sell to maximize profit?

4,100

Step-by-step explanation:

Let x be increase in the price % and f(x) be revenue

Revenue = Sales price*Total number hot dog sold

Hot dog sold = $4/dog

Now when increase in $0.25. Then, Revenue f(x) = (4+0.25x) (500 - 200x)

f(x) = 2000 - 800x + 1250x - 50x^2

f(x) = -50x^2 + 450x + 2000

To maximize revenue, we have to find f1(x) and find the value of x for which f1(x) = 0

f1(x) = -100x + 450

0 = 0100x + 450

x = 4.5

Hence, to maximize profit number of hot dog they sell: 5000 - 200(4.5)

= 5000 - 900

= 4100

Thus, the number of hot dog sold = 4,100

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.