Question

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?

Answer 1

4,100

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