Answer:
![C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2](https://tex.z-dn.net/?f=C%28x%29%3D500%2B20x-5x%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%2B0.01x%5E2)
![p(x)=320-7.7p](https://tex.z-dn.net/?f=p%28x%29%3D320-7.7p)
![R(x)=(320-7.7p)p=320p-7.7p^2](https://tex.z-dn.net/?f=R%28x%29%3D%28320-7.7p%29p%3D320p-7.7p%5E2)
![x=82 \text{planes}](https://tex.z-dn.net/?f=x%3D82%20%5Ctext%7Bplanes%7D)
![p=\$30.91 M\;\; \text{per plane}](https://tex.z-dn.net/?f=p%3D%5C%2430.91%20M%5C%3B%5C%3B%20%5Ctext%7Bper%20plane%7D)
maximum profit ![=\$ 15.90M](https://tex.z-dn.net/?f=%3D%5C%24%2015.90M)
Step-by-step explanation:
Given that,
The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.
The additional cost of manufacturing each plane can be modelled by the function.
![m(x)=20x-5x^{\frac{3}{4}}+0.01x^2](https://tex.z-dn.net/?f=m%28x%29%3D20x-5x%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%2B0.01x%5E2)
Find the cost, demand (or price), and revenue functions.
![C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2](https://tex.z-dn.net/?f=C%28x%29%3D500%2B20x-5x%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%2B0.01x%5E2)
![p(x)=320-7.7p](https://tex.z-dn.net/?f=p%28x%29%3D320-7.7p)
![R(x)=(320-7.7p)p=320p-7.7p^2](https://tex.z-dn.net/?f=R%28x%29%3D%28320-7.7p%29p%3D320p-7.7p%5E2)
Find the production level that maximizes profit.
![f=R(x)-C(x)](https://tex.z-dn.net/?f=f%3DR%28x%29-C%28x%29)
![\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)](https://tex.z-dn.net/?f=%5CRightarrow%20f%3D320p-7.7p%5E2-%28500%2B20x-5x%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%2B0.01x%5E2%29)
![\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx](https://tex.z-dn.net/?f=%5CRightarrow%20df%3D320dp-15.4pdp-20dx%2B5%28%5Cfrac%7B3%7D%7B4%7D%20%29x%5E%7B%5Cfrac%7B-1%7D%7B4%7D%20%7Ddx-0.02xdx)
![x=320-7.7p](https://tex.z-dn.net/?f=x%3D320-7.7p)
![p=\frac{320-x}{7.7}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B320-x%7D%7B7.7%7D)
![\frac{dp}{dx} = \frac{-1}{7.7}](https://tex.z-dn.net/?f=%5Cfrac%7Bdp%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-1%7D%7B7.7%7D)
![\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0](https://tex.z-dn.net/?f=%5Cfrac%7Bdf%7D%7Bdx%7D%3D%5Cfrac%7B320%7D%7B-7.7%7D%20-%5Cfrac%7B15.4%28320-x%29%20%7D%7B7.7%28%5Cfrac%7B-1%7D%7B7.7%7D%20%29%7D-20%2B5%5Cfrac%7B3%7D%7B4%7D%20x%5E%7B%5Cfrac%7B-1%7D%7B4%7D%7D%20-0.02x%3D0)
![\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0](https://tex.z-dn.net/?f=%5CRightarrow%20-41.5584%2B83.1169-0.2597x-20%2B3.75x%5E%7B%5Cfrac%7B-1%7D%7B4%7D%20%7D-0.02x%3D0)
![\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0](https://tex.z-dn.net/?f=%5CRightarrow%2021.5585%2B3.75x%5E%7B%5Cfrac%7B-1%7D%7B4%7D%20%7D-0.279x%3D0)
![\Rightarrow x=82 \text{planes}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D82%20%5Ctext%7Bplanes%7D)
Find the associated selling price of the aircraft that maximizes profit.
![p=\frac{320-82}{7.7}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B320-82%7D%7B7.7%7D)
![\Rightarrow p=\$30.91 M\;\; \text{per plane}](https://tex.z-dn.net/?f=%5CRightarrow%20p%3D%5C%2430.91%20M%5C%3B%5C%3B%20%5Ctext%7Bper%20plane%7D)
Find the maximum profit.
Manufacturing cost of one plane is:
![m(1)=20-5+0.01](https://tex.z-dn.net/?f=m%281%29%3D20-5%2B0.01)
![=\$15.01 M](https://tex.z-dn.net/?f=%3D%5C%2415.01%20M)
maximum profit ![=\$(30.91-15.01)M](https://tex.z-dn.net/?f=%3D%5C%24%2830.91-15.01%29M)
![=\$15.90M](https://tex.z-dn.net/?f=%3D%5C%2415.90M)
C is correct. So it’s asking given any whole number Squared you will get another whole number squared but in reality there are only a few numbers like that and they are called perfect squares(4 16 36 81 121)
Answer:
The workers will need 10 days to finish the job.
Step-by-step explanation:
To solve this question we can use a compound rule of three. We have:
10 road workers -> 5 days -> 2h/day
2 road workers -> x days -> 5h/days
The first thing we should do is analyze how the proportions between the variables work, if they're inversely or directly proportional. If we raise the number of workers we expect that the amount of days needed to finish the job lowers and if we raise the number of hours worked in a day we expect that the workers would need less days to finish the job. So we need to invert the fractions that are inversely proportional to the amount of days worked, then we have:
2 -> 5 -> 5
10-> x -> 2
x = (5*2*10)/(2*5) = 100/10 = 10 days
Answer:
245
Step-by-step explanation:
$49.00 times 5 is 245. The 5 came from the question because it says a normal work week has 5 days so you would multiply $49.00 by 5