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 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.).
a What are we going to sell?
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b What does each item cost to make or purchase?
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c How much will we sell each item for?
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d How much will you invest in your business?
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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?
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c. Graph your inequality. Be sure to label your graph and shade the appropriate side of the line.
a
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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.
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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.
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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.
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Task 1:
a. Business Explanation:
- I am starting a business selling handmade jewelry and custom-made keychains.
- I am willing to invest $2000 of my own money into this business.
- Each handmade jewelry item costs $10 to make.
- Each custom-made keychain costs $5 to make.
- I will sell each handmade jewelry item for $30 and each custom-made keychain for $15.
b. Inequality:
Let x represent the number of handmade jewelry items and y represent the number of custom-made keychains.
The inequality representing the cost limit is:
10x + 5y ≤ 2000
c. Graph of Inequality:
(To be provided by the user)
d. Point in the shaded region:
If we choose the point (100, 200), it falls in the shaded region.
The x-coordinate represents the number of handmade jewelry items (100) and the y-coordinate represents the number of custom-made keychains (200). The significance is that the cost of producing 100 handmade jewelry items and 200 custom-made keychains falls within the investment limit of $2000.
e. Point on the line:
If we choose the point (200, 200), it falls directly on the line.
The x-coordinate represents the number of handmade jewelry items (200) and the y-coordinate represents the number of custom-made keychains (200). The significance is that the cost of producing 200 handmade jewelry items and 200 custom-made keychains exactly equals the investment limit of $2000.
f. Point outside the shaded region:
If we choose the point (150, 250), it falls outside the shaded region.
The x-coordinate represents the number of handmade jewelry items (150) and the y-coordinate represents the number of custom-made keychains (250). The significance is that the cost of producing 150 handmade jewelry items and 250 custom-made keychains exceeds the investment limit of $2000.