Task 1
You are starting a new business in which you have decided to sell two products instead of just one. Determine a business you could start and choose two products that you could sell. How much of your own money are you willing to invest in this
business to get started? How much will each item cost you to make? How much will
you charge for each item?
a. Explain this business (how much of your own money you’re willing to spend on the business, what items you’re going to sell, costs for each item, sale price for each item, etc.).
a What are we going to sell?
b What does each item cost to make or purchase?
c How much will we sell each item for?
d How much will you invest in your business?
b. Write an inequality that represents the fact that while making each item, you can’t exceed this limit. Be sure to include the cost per item in this inequality.
a What is the inequality for your business plan?
c. Graph your inequality. Be sure to label your graph and shade the appropriate side of the line.
d. Choose a point that falls in the shaded region. Explain what the x-coordinate and y-coordinate represent and the significance in terms of cost of this point falling in the shaded region.
e. Choose a point that falls directly on the line. Explain what the x-coordinate and y-coordinate represent and the significance in terms of cost of this point falling directly on the line.
f. Choose a point that does not fall in the shaded region. Explain what the x-coordinate and y-coordinate represent and the significance in terms of cost of this point falling outside of the shaded region.
a. I am starting a new business selling handcrafted jewelry. I am willing to invest $5,000 of my own money to get started. I will be selling two products: beaded necklaces and beaded bracelets. The cost to make each necklace is $10 and the cost to make each bracelet is $5. I plan to sell each necklace for $25 and each bracelet for $15.
b. Inequality: 10x + 5y ≤ 5000
c. Graph:
The graph of the inequality is a straight line with the x-intercept at 500 and the y-intercept at 1000. The shaded region is below the line.
d. Point in shaded region: (200, 300)
Explanation: The x-coordinate (200) represents the number of necklaces made, and the y-coordinate (300) represents the number of bracelets made. This point falls within the cost constraint, meaning that making 200 necklaces and 300 bracelets would not exceed the $5,000 investment.
e. Point on the line: (500, 0)
Explanation: The x-coordinate (500) represents the number of necklaces made, and the y-coordinate (0) represents the number of bracelets made. This point falls directly on the line, meaning that making 500 necklaces would use up the entire $5,000 investment.
f. Point outside shaded region: (600, 200)
Explanation: The x-coordinate (600) represents the number of necklaces made, and the y-coordinate (200) represents the number of bracelets made. This point falls outside the shaded region, meaning that making 600 necklaces and 200 bracelets would exceed the $5,000 investment.