Answer:
Given :
At the Burger Palace you earn $8 per hour.
At the community center you teach soccer clinics for $10 per hour.
You want to earn at least $200 a week.
To Find: which graph shows all the ways you can earn at least $200 a week?
Solution:
Let x is the number of hours you work at Burger Palace
At the Burger Palace you earn $8 per hour.
So, At the Burger Palace you earn in x hour = 8x
Let y is the number of hours you work
At the community center you teach soccer clinics for $10 per hour.
So, At the community center you teach soccer clinics earns in x hour = 10x
Now we are given that You want to earn at least $200 a week. (i.e. $200 or more than $200)
So, equation becomes:[tex]8x+10y\geq 200[/tex]
At x = 0
[tex]8(0)+10y\geq 200[/tex]
[tex]y\geq 20[/tex]
At y = 0
[tex]8x+10(0)\geq 200[/tex]
[tex]x\geq 25[/tex]
Thus the points are (0,20) and (25,0)
At(0,0)
[tex]8(0)+10(0)\geq 200[/tex]
[tex]0\geq 200[/tex] False
Thus the feasible region is away from the origin
So, Option 2 graph is true (Figure attached).
