How am I supposed to solve and construct a graph for this problem?
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."
To solve this problem and construct a graph, you can follow these steps:
Step 1: Determine the variables: In this problem, the variables are the number of cups of lemonade (L) and the number of cupcakes (C) that Sandy sells.
Step 2: Identify the constraints: Sandy wants to sell at least 5 cups of lemonade and at least 5 cupcakes per day, and she wants to earn at least $25 per day.
Step 3: Set up the inequalities: Based on the constraints, we can set up the following inequalities:
2L + C ≥ 25 (the total profit should be at least $25 per day)
L ≥ 5 (at least 5 cups of lemonade)
C ≥ 5 (at least 5 cupcakes)
Step 4: Construct a graph: On a coordinate plane, plot the points that satisfy the three inequalities. To do this, you can start by plotting the points that satisfy each individual inequality, and then shade the region that satisfies all three.
Step 5: Describe the possible combinations: Look for the overlapping shaded region on the graph. Each point in this region represents a combination of lemonade and cupcakes that meets Sandy's goals. You can describe these combinations by reading the values of L (lemonade) and C (cupcakes) from the points in the overlapping shaded region.
For example, two possible combinations could be:
Combination 1: L = 5 cups of lemonade, C = 20 cupcakes
Combination 2: L = 15 cups of lemonade, C = 5 cupcakes
These combinations satisfy the constraints of selling at least 5 cups of lemonade and at least 5 cupcakes, and earning at least $25 per day.
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