Answer:
I think it is A but not 100% sure.
Step-by-step explanation:
Answer:
4.002 x 10^3
Step-by-step explanation:
Answer:
a) The demand function is
![q(p) = -4 p + 107](https://tex.z-dn.net/?f=q%28p%29%20%3D%20-4%20p%20%2B%20107)
b) The nightly revenue is
![R(p) = -4 p^2 + 107 p](https://tex.z-dn.net/?f=%20R%28p%29%20%3D%20-4%20p%5E2%20%2B%20107%20p%20)
c) The profit function is
![P(p) = -4 p^2 + 133.75 p - 939](https://tex.z-dn.net/?f=P%28p%29%20%3D%20-4%20p%5E2%20%2B%20133.75%20p%20-%20939%20)
d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.
Step-by-step explanation:
a) Lets find the slope s of the demand:
![s = \frac{79-43}{7-16} = \frac{36}{-9} = -4](https://tex.z-dn.net/?f=%20s%20%3D%20%5Cfrac%7B79-43%7D%7B7-16%7D%20%3D%20%5Cfrac%7B36%7D%7B-9%7D%20%3D%20-4%20)
Since the demand takes the value 79 in 7, then
![q(p) = -4 (p-7) + 79 = -4 p + 107](https://tex.z-dn.net/?f=q%28p%29%20%3D%20-4%20%28p-7%29%20%2B%2079%20%3D%20-4%20p%20%2B%20107)
b) The nightly revenue can be found by multiplying q by p
![R(p) = p*q(p) = p*( -4 p + 107) = -4 p^2 + 107 p](https://tex.z-dn.net/?f=R%28p%29%20%3D%20p%2Aq%28p%29%20%3D%20p%2A%28%20-4%20p%20%2B%20107%29%20%3D%20-4%20p%5E2%20%2B%20107%20p)
c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)
![P(p) = R(p) - C(p) = p*q(p) = -4 p^2 + 107 p - (-26.75p + 939) = \\\\-4 p^2 + 133.75 p - 939](https://tex.z-dn.net/?f=P%28p%29%20%3D%20R%28p%29%20-%20C%28p%29%20%3D%20p%2Aq%28p%29%20%3D%20-4%20p%5E2%20%2B%20107%20p%20-%20%28-26.75p%20%2B%20939%29%20%3D%20%5C%5C%5C%5C-4%20p%5E2%20%2B%20133.75%20p%20-%20939)
d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P
![r_1, r_2 = \frac{-133.75 \,^+_-\, \sqrt{133.75^2-4*(-4)*(-939)} }{-8} = \frac{-133.75 \,^+_-\, 53.526}{-8} \\r_1 = 10.03\\r_2 = 23.41](https://tex.z-dn.net/?f=r_1%2C%20r_2%20%3D%20%5Cfrac%7B-133.75%20%5C%2C%5E%2B_-%5C%2C%20%5Csqrt%7B133.75%5E2-4%2A%28-4%29%2A%28-939%29%7D%20%7D%7B-8%7D%20%3D%20%5Cfrac%7B-133.75%20%5C%2C%5E%2B_-%5C%2C%2053.526%7D%7B-8%7D%20%5C%5Cr_1%20%3D%2010.03%5C%5Cr_2%20%3D%2023.41)
Therefore, the entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.
85700, 8570, 857, 85.7, 8.57, .857
2((x+2)(x+2)}-4=28
2{x^2 + 4x + 4}-4=28
2x^2 +4x=28
2(x^2+2x)=28
x^2+2x=28/2
x^2+2x=14