How am I supposed to solve and construct a graph for this problem?

Question

1. Sandy makes $2 profit on every cup of lemonade that she sells and $1 on every cupcake that she sells. Sandy wants to sell at least 5 cups of lemonade and at least 5 cupcakes per day. She wants to earn at least $25 per day. Show and describe all the possible combinations of lemonade and cupcakes that sandy needs to sell to meet her goals. List two possible combinations."

Anonymous · Answer

if she sells x lemonades and y cupcakes, then we have

x >= 5
y >= 5
2x+y >= 25

suppose she sells 5 lemonades. That makes $10. So she needs at least 15 cupcakes to get to $25.

Each extra lemonade she sells makes her an additional $2, so she can sell 2 fewer cupcakes. So, we can have

x=5 y=15
x=6 y=13
...
x=10 y=5

Sloan Smith · Answer

I just graph the two equations and then find which way in a direction it points. Then any order pair in the in-between of those two directions will be one of the answers!