B............................................:::/::::/:::::::
Answer:
a) p(x)=-0.0006x +21.6
b) $10.80
Step-by-step explanation:
a) Assuming that p(x) is linear, the slope can be found by:
![m=\frac{\$9-\$6}{21000-26000} \\m=-0.0006](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%5C%249-%5C%246%7D%7B21000-26000%7D%20%5C%5Cm%3D-0.0006)
Applying the point (21000; $9) to the general linear equation gives us the demand function:
![(p-p_0)=m(x-x_0)\\(p-9)=-0.0006(x-21,000)\\p(x)=-0.0006x +21.6](https://tex.z-dn.net/?f=%28p-p_0%29%3Dm%28x-x_0%29%5C%5C%28p-9%29%3D-0.0006%28x-21%2C000%29%5C%5Cp%28x%29%3D-0.0006x%20%2B21.6)
b) Revenue is given by the number of tickets sold multiplied by the price, the revenue function is:
![R(x) = xp(x)\\R(x) = -0.0006x^2 +21.6x](https://tex.z-dn.net/?f=R%28x%29%20%3D%20xp%28x%29%5C%5CR%28x%29%20%3D%20-0.0006x%5E2%20%2B21.6x)
The value of x for which the revenue function's derivate is zero is the number of spectators that yield the maximum revenue:
![\frac{dR(x)}{dx} = -0.0012x +21.6 = 0\\x=\frac{21.6}{0.0012}\\x= 18,000](https://tex.z-dn.net/?f=%5Cfrac%7BdR%28x%29%7D%7Bdx%7D%20%3D%20-0.0012x%20%2B21.6%20%3D%200%5C%5Cx%3D%5Cfrac%7B21.6%7D%7B0.0012%7D%5C%5Cx%3D%2018%2C000)
At x = 18,000, tickets price are:
![p(18,000)=-0.0006*18,000 +21.6\\p = \$10.80](https://tex.z-dn.net/?f=p%2818%2C000%29%3D-0.0006%2A18%2C000%20%2B21.6%5C%5Cp%20%3D%20%5C%2410.80)
Answer:
m<8 = 130
m<6 = 130
m<7 = 50
m<11 = 65
m<15 = 65
m<10 = 65
Step-by-step explanation:
Answer:
360
Step-by-step explanation:
Answer:
x=8
Step-by-step explanation:
9 3
---- = -----
24 x
Using cross products
9 * x = 3 * 24
Divide each side by 9
9x/9 = 3*24/9
x = 3/9 * 24
x = 1/3 *24
x = 8