Systems of Equations and Inequalities Portfolio (12 Points)
To receive full credit, yourSystems of Equations and Inequalities Portfolio must include ALL of the following:
TASK 1 (6 points)
You are starting a new business in which you are selling TWO products. Spend some time thinking about these questions and then fill in your answers below to help you set up your business: What business could you start, what TWO products could you sell? Before you made any money from selling your products, how much of your own money are you willing to put into this business to help get it started? Think of how much each item will cost you to make.
Topic
Answer
Explain your business by answering the following:
What TWO items will you be selling?
How much of your own money are you willing to spend to get it started (start up amount)?
What is the cost to make Item #1?
What is the cost to make Item #2?
Shirts and pants
1000
400
600
Write an INEQUALITY that represents your costs considering what you are willing to spend on the business start up.
Example:
(cost to make item#1)x + (cost to make item #2)y start up amount
Graph your inequality either by hand or using Desmos. Put a screenshot of it here:
Choose a point that falls in the shaded region.
What point did you choose?
What do the x and y-coordinate represent in context?
Is this a combination you can afford to make? Explain.
Choose a point that falls exactly ON the line.
What do the x and y-coordinate represent in context?
Is this a combination you can afford to make? Explain.
d.
e.
Choose a point that does not fall in the shaded region.
What point did you choose?
What do the x and y-coordinate represent in context?
Is this a combination you can afford to make? Explain.
f.
g.
h.
Bonus Point: Do points in Quadrant II, III, or IV make sense in the context of this problem? Explain. (+1)
TASK 2 (4 points)
Now that we have worked through what your cost will be, let’s think about how much you will sell each item for. The goal is to earn a total amount that is AT LEAST TWICE the amount you spend on start up costs.
Topic
Answer
How much money are you hoping to earn from selling your products?
How much will you sell Item #1 for?
How much will you sell Item #2 for?
Write an inequality that represents the fact that you want your total earned to be at least two times the amount that you originally spent. The price you are going to sell each item at should be included in this inequality.
Graph the inequality using Desmos and put a screenshot here.
Note: If the shaded region doesn’t make sense, adjust your values for what you will sell each item for or what you are putting in as a start up amount.
Choose a point that falls in the shaded region.
What point did you choose?
What does the x and y-coordinate represent in context?
TASK 3 (2 points)
Put it all together:
Topic
Answer
Put the graph from Task 1 and the graph from Task 2 on the same coordinate plane using Desmos. Put a screenshot here:
Choose a point that falls in the shaded region for both inequalities. Explain what the x and y-coordinate represent in context. Also, explain the significance of this point in terms of cost and money earned as it relates to the shaded regions.