Task 1. You want to start a summer business to earn money. What will you do? You have to consider how much money you can afford to invest in this business how much it will cost you to make each item and how much you're going to charge for each item. Research something that would be reasonable to make and sell with the start up investment you have determined.
Task 2. In task 1 you determined how much of your own money you're willing to spend to get your business started. This is your limit- when making your product you can't exceed this amount.
a. Write an inequality that represents the fact that while making your product you can't exceed this spending limit
b. Solve this inequality and graph solution on a number line. Explain what your solution means in terms of the situation.
c. In task 1. You determined how much you will charge for each item. Write an equation that represents your total earnings based on the price of your item and how many you sell.
d. Using your answer from part B and your equation from part C, what is the most money you can hope to earn from your business?
e. Don't forget that at the beginning of the process you had to spend some of your own money to get started. With the costs taken into account, what was your total profit? Did you make money or lose money? Now that you have these values, would you adjust your business plan from task 1? If so, how?
TASK 3. You parents heard about the success of your business and they want to help you out. Suppose they want to give you an additional $300 to put toward your business. However, there's a catch. If you make more than $600 total, you have to give them 10% of your earnings above $600. For example, if you have earned $650, then you owe 10% or $50 or $5, to your parents.
a. Now that you have an additional $300, revise your inequality from part A of task 2 to reflect your new spending limit. Solve this inequality and graph the solution on a number line. Explain what you solution means in terms of the situation.
b. If you still sell your item for the same price, what is the most money you can hope to make from your business now?
c. Will you have to pay your parents? If so, determine how much you will owe them.
d. Think about how much time it will take you to create your product. You have 200 hours this summer to devote to creating your product. Write an inequality that represents your time constraint.
e. Solve your inequality from part D and graph your solution on a number line. Explain what your solution means in terms of the situation.
f. With the costs taken into account, what was your total profit? Did you make or lose money? Now that you have these values, would you adjust your business plan from task 1?if so, how?
IM on the same thing stuck on task 2
Task 1:
To start a summer business and earn money, you need to consider the following factors:
1. Determine your investment budget: Assess how much money you can afford to invest in the business. This budget will help you determine the maximum amount you can spend on producing the items.
2. Calculate production cost: Research different products or services that can be reasonably made and sold within your investment budget. Determine the cost of making each item, including raw materials, labor, and any other expenses involved.
3. Set the selling price: Based on market research and competition, determine a reasonable selling price for each item. This price should allow you to cover your production costs and make a profit.
Task 2:
a. Write an inequality: Let's assume your spending limit, determined in Task 1, is represented by the variable "L." The inequality would be: Cost per item ≤ L.
b. Solve the inequality: Solve the inequality by isolating the variable "Cost per item" on one side. For example, if the cost per item is represented by the variable "C," the inequality would become C ≤ L. Graphically, this would be shown as a shaded region on a number line to the left of or on the point L.
The solution in terms of the situation means that the cost per item cannot exceed the spending limit. It ensures that you stay within your budget while producing the items for your business.
c. Total earnings equation: Let the price per item be denoted by "P," and the number of items sold be denoted by "N." The equation for total earnings would be: Total earnings = P * N.
d. Determine maximum earnings: Using the result from part b, multiply the maximum number of items you can produce/sell, represented by "M," with the price per item, P. The equation would be: Maximum earnings = P * M.
e. Calculate total profit: To determine the total profit, subtract the total cost of producing all items from the maximum earnings. If the resulting value is positive, you made money; if it's negative, you lost money. Based on these values, you can determine whether adjustments to your business plan in Task 1 are needed, such as reducing costs or increasing prices.
Task 3:
a. Revise the inequality: Since your parents want to contribute an additional $300, the revised spending limit would be L + 300. The inequality would become Cost per item ≤ L + 300.
b. Maximum earnings with the new spending limit: Use the solution from part a to determine the maximum number of items you can produce/sell. Multiply this with the price per item, P. The equation would be: Maximum earnings = P * (Maximum number of items).
c. Determine payment to parents: If your total earnings exceed $600, calculate 10% of the earnings above $600 to determine how much you owe your parents.
For example, if your earnings are represented by "E," the payment owed to your parents would be: Payment = 10% * (E - 600). This equation calculates 10% of the amount earned over $600.
d. Time constraint inequality: Let "T" represent the time in hours needed to create each item, and "H" represent the total available time (200 hours). The corresponding inequality would be T * N ≤ H, where N denotes the number of items you plan to produce.
e. Solve the inequality: Solve the inequality T * N ≤ H to determine the maximum number of items you can produce/sell. Graphically, this would be shown as a shaded region on a number line to the left of or on the point H.
The solution in terms of the situation means that the total time required to create the items cannot exceed the available time limit.
f. Calculate total profit: Subtract the total cost of producing all items from the maximum earnings, taking into account the adjustments made in part c and part e. Determine whether you made or lost money. Based on these values, you can decide whether any adjustments are needed to your business plan from Task 1, such as optimizing production time or reevaluating profits.
Task 1:
1. Determine how much money you can afford to invest in your summer business.
2. Calculate how much it will cost you to make each item.
3. Research something that would be reasonable to make and sell within your startup investment.
4. Determine how much you will charge for each item.
Task 2:
a. Write an inequality that represents the fact that while making your product, you can't exceed your spending limit.
Let's say your spending limit is "x". The inequality would be: Cost per item <= x
b. Solve the inequality and graph the solution on a number line. Explain what your solution means in terms of the situation.
The solution to the inequality would be a range of values that represent the cost per item being less than or equal to your spending limit. On a number line, this would be represented as a shaded region to the left of or on the point that represents your spending limit. This means that the cost per item cannot exceed your spending limit.
c. Write an equation that represents your total earnings based on the price of your item and how many you sell.
Let's say the price per item is "p" and the quantity sold is "q". The equation for total earnings would be: Total earnings = p * q
d. Using your answer from part B and your equation from part C, calculate the most money you can hope to earn from your business.
This would be the maximum value you can achieve for total earnings based on the price per item, quantity sold, and the solution to the inequality in part B.
e. Calculate your total profit by subtracting your initial investment from your total earnings. Determine if you made money or lost money. Based on these values, decide if you need to adjust your business plan from task 1.
Task 3:
a. Revise the inequality from part A of task 2 to reflect your new spending limit with the additional $300 from your parents.
Let's say the new spending limit is "y". The revised inequality would be: Cost per item <= y
b. If you still sell your item for the same price, calculate the most money you can hope to make from your business now.
This would be the maximum value you can achieve for total earnings based on the new spending limit, price per item, and quantity sold.
c. Determine if you have to pay your parents, and if so, calculate how much you owe them.
If your total earnings exceed $600, you owe your parents 10% of the amount above $600. Calculate this amount based on your total earnings.
d. Write an inequality that represents your time constraint. Let's say the total time available is "t" and the time spent per item is "s". The inequality would be: s * q <= t, where q is the quantity sold.
e. Solve the inequality from part D and graph the solution on a number line. Explain what your solution means in terms of the situation.
The solution to the inequality would be a range of values that represent the quantity sold multiplied by the time spent per item being less than or equal to the total time available. On a number line, this would be represented as a shaded region to the left of or on the point that represents the total time available. This means that the time spent creating each item cannot exceed the total time available.
f. Calculate your total profit by subtracting your initial investment, additional investment from your parents, and any amount owed to your parents from your total earnings. Determine if you made or lost money. Based on these values, decide if you need to adjust your business plan from task 1.