<u>Answer-</u>
Set of constraints to model the problem are,
![12x+9y\geq 510](https://tex.z-dn.net/?f=12x%2B9y%5Cgeq%20510)
![y \leq 2x](https://tex.z-dn.net/?f=y%20%5Cleq%202x)
![y \geq 25](https://tex.z-dn.net/?f=y%20%5Cgeq%2025)
<u>Solution-</u>
<em>x = the number of lawns weeded by Gwen,</em>
<em>y = the number of dogs walked by Fabio.</em>
1.
As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,
![\text{Earnings of Gwen} = 12x](https://tex.z-dn.net/?f=%5Ctext%7BEarnings%20of%20Gwen%7D%20%3D%2012x)
![\text{Earnings of Fabio} = 9y](https://tex.z-dn.net/?f=%5Ctext%7BEarnings%20of%20Fabio%7D%20%3D%209y)
![\text{Total earning} = 12x+9y](https://tex.z-dn.net/?f=%5Ctext%7BTotal%20earning%7D%20%3D%2012x%2B9y)
They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.
The equation for this is,
![12x+9y\geq 510](https://tex.z-dn.net/?f=12x%2B9y%5Cgeq%20510)
2.
The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means
y must be less than or equal to 2x.
The equation for this is,
![y \leq 2x](https://tex.z-dn.net/?f=y%20%5Cleq%202x)
3.
Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.
The equation for this is,
![y \geq 25](https://tex.z-dn.net/?f=y%20%5Cgeq%2025)