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 in order 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.).
b. Consider the total amount you’re willing to spend on the business and how
much it will cost you to make your items. 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.
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 xcoordinate 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 where I am willing to invest $10,000 of my own money. I have decided to sell handmade jewelry and natural skincare products. The cost to make each piece of jewelry is $5, and the sale price for each piece is $15. The cost to make each skincare product is $10, and the sale price for each product is $25.
b. The total amount I am willing to spend on the business is $10,000. Let's represent the number of jewelry pieces as 'x' and the number of skincare products as 'y'. The inequality representing the cost limit would be:
5x + 10y ≤ 10,000
c. To graph this inequality, we can create a coordinate plane with 'x' representing the quantity of jewelry pieces and 'y' representing the quantity of skincare products. The x-axis represents the number of jewelry pieces, and the y-axis represents the number of skincare products. The shaded region should be below or on the line 5x + 10y = 10,000.
d. Let's choose the point (1000, 500) that falls in the shaded region. The x-coordinate represents the quantity of jewelry pieces (1000) and the y-coordinate represents the quantity of skincare products (500). The significance of this point falling in the shaded region is that the total cost of producing 1000 jewelry pieces and 500 skincare products is within the $10,000 investment limit.
e. Let's choose the point (2000, 800) that falls directly on the line. The x-coordinate represents the quantity of jewelry pieces (2000) and the y-coordinate represents the quantity of skincare products (800). The significance of this point falling on the line is that the total cost of producing 2000 jewelry pieces and 800 skincare products exactly matches the $10,000 investment limit.
f. Let's choose the point (3000, 400) that does not fall in the shaded region. The x-coordinate represents the quantity of jewelry pieces (3000) and the y-coordinate represents the quantity of skincare products (400). The significance of this point falling outside the shaded region is that the total cost of producing 3000 jewelry pieces and 400 skincare products exceeds the $10,000 investment limit.