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Anna71 [15]
3 years ago
8

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, the

y will sell 200 less dogs. How many hot dogs should they sell to maximize profit?
Mathematics
1 answer:
Xelga [282]3 years ago
7 0

Answer:

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

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