Solve the system of equations from part A.
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What method did you choose to solve the system?
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Explain what your solution for part D means in terms of the situation.
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Part A: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?
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.).
What are we going to sell?
I will sell custom-made photo frames and engraved jewelry.
What does each item cost to make or purchase?
Cost for each item:
- Photo frame: $10
- Engraved jewelry: $15
How much will we sell each item for?
Sale price for each item:
- Photo frame: $25
- Engraved jewelry: $40
How much will you invest in your business?I am willing to invest $5,000 of my own money to get started with this business.
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.
What is the inequality for your business plan?
I plan to invest in materials and equipment to make custom photo frames and engraved jewelry. With my initial investment of $5,000, I will purchase the necessary tools, supplies, and marketing materials. The cost to make each photo frame is $10, and I will sell them for $25 each, making a profit of $15 per frame.
Part B: Task 2
Now that we know what business you’re going to start, let’s plan what you need to buy to start your business. You will need a maximum of 500 photo frames and jewelry items to sell. Write an inequality that represents this scenario.
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How many of each item can you afford to make with the money you have to start your business? Write this inequality in terms of the cost to make each item and your budget.
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Part C: Task 3
Let’s say you will need to rent a space to make your photo frames and jewelry. For rent, utilities, and other business expenses, it will cost you $300 a month. Determine how many items you need to sell each month to cover those expenses.
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Part D: Task 4
To make a profit, I need to sell all of my items, but I want to make a greater profit from the jewelry. Let’s say I make $15 profit from each photo frame and $25 profit from each jewelry item. Write a system of equations to represent this situation.
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Solve the system of equations from part A.
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What method did you choose to solve the system?
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Explain what your solution for part D means in terms of the situation.
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