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2 answers:
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Answer:
(a)
(b)
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
Therefore, we have:
At point (12,30000)
Therefore:
(b)Revenue
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
Therefore:
- Optimal ticket price:$12
- Maximum Revenue:$360,000
Answer:
<h2>A = 57</h2>Step-by-step explanation:
Use the Pick's theorem
Let P be a polygon in the plane whose vertices have integer coordinates. Then the area of P can be determined just by counting the lattice points on the interior and boundary of the polygon!
In fact, the area is given by
where <em>i</em> is the number interior lattice points, and<em> b</em> is the number of boundary lattice points.
Look at the picture.
Substitute:
