-3x + 18 = 7x
3x + (-3x) + 18= 7x + 3x
18 = 10x
18 10x
— = —
10 10
1.8 = x
20/18+5/18=25/18
25/18 can be written as mixed fraction 1 7/18
This can be solve by just dividing the total money that prince
paid to kathy by the yearly dividend per share of stock. Since prince waste
collection pays kathy $46,926.54 in dividends every year and divide it by $14.94.
so kathy owns 3141 share of stocks
Answer:
Step-by-step explanation:
Given
Cost Price ![c(x)=72000+60x](https://tex.z-dn.net/?f=c%28x%29%3D72000%2B60x)
Price ![p(x)=300-\frac{x}{20}](https://tex.z-dn.net/?f=p%28x%29%3D300-%5Cfrac%7Bx%7D%7B20%7D)
Revenue generated ![R(x)=P(x)\times x](https://tex.z-dn.net/?f=R%28x%29%3DP%28x%29%5Ctimes%20x)
where x=no of units
![R(x)=300x-\frac{x^2}{20}](https://tex.z-dn.net/?f=R%28x%29%3D300x-%5Cfrac%7Bx%5E2%7D%7B20%7D)
To get maxima and minima differentiate R(x)
![\frac{\mathrm{d} R(x)}{\mathrm{d} x}=0](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20R%28x%29%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D0)
![\frac{\mathrm{d} R(x)}{\mathrm{d} x}=300-2\times \frac{x}{20}=0](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20R%28x%29%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D300-2%5Ctimes%20%5Cfrac%7Bx%7D%7B20%7D%3D0)
![300=2\times \frac{x}{20}](https://tex.z-dn.net/?f=300%3D2%5Ctimes%20%5Cfrac%7Bx%7D%7B20%7D)
![x=3000](https://tex.z-dn.net/?f=x%3D3000)
maximum Revenue ![R(x)=(300-\frac{300}{20})\times 300=4,50,000](https://tex.z-dn.net/?f=R%28x%29%3D%28300-%5Cfrac%7B300%7D%7B20%7D%29%5Ctimes%20300%3D4%2C50%2C000%20)
(b)Profit=Revenue - cost
![Profit=xp(x)-c(x)](https://tex.z-dn.net/?f=Profit%3Dxp%28x%29-c%28x%29)
![Profit=300x-\frac{x^2}{20}-72000-60x](https://tex.z-dn.net/?f=Profit%3D300x-%5Cfrac%7Bx%5E2%7D%7B20%7D-72000-60x)
![Profit(z)=240x-\frac{x^2}{20}-72000](https://tex.z-dn.net/?f=Profit%28z%29%3D240x-%5Cfrac%7Bx%5E2%7D%7B20%7D-72000)
differentiate Profit to get maximum value
![\frac{\mathrm{d} z}{\mathrm{d} x}=240-2\times \frac{x}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20z%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D240-2%5Ctimes%20%5Cfrac%7Bx%7D%7B20%7D)
![x=2400](https://tex.z-dn.net/?f=x%3D2400)
maximum Profit ![z=2,16,000](https://tex.z-dn.net/?f=z%3D2%2C16%2C000)
(c)Now company decided to tax the company $ 55 for each set
Profit ![(z_1)=xp(x)-c(x)-55x](https://tex.z-dn.net/?f=%28z_1%29%3Dxp%28x%29-c%28x%29-55x)
![z_1=300x-\frac{x^2}{20}-72000x-60x^2-55x](https://tex.z-dn.net/?f=z_1%3D300x-%5Cfrac%7Bx%5E2%7D%7B20%7D-72000x-60x%5E2-55x)
![z_1=185x-\frac{x^2}{20}-72,000](https://tex.z-dn.net/?f=z_1%3D185x-%5Cfrac%7Bx%5E2%7D%7B20%7D-72%2C000)
differentiate Profit to get maximum value
![\frac{\mathrm{d} z_1}{\mathrm{d} x}=0](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20z_1%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D0)
![\frac{\mathrm{d} z_1}{\mathrm{d} x}=185-\frac{2x}{20}=0](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20z_1%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D185-%5Cfrac%7B2x%7D%7B20%7D%3D0)
![x=1850](https://tex.z-dn.net/?f=x%3D1850)
![P(z_1\ at\ x=1850)=99125](https://tex.z-dn.net/?f=P%28z_1%5C%20at%5C%20x%3D1850%29%3D99125)
company should charge 207.5 $ for each set