Question

Angela engages in a bracelet-making business where she crafts each bracelet for 65 cents and sells them online for $2.00 each. Additionally, Angela incurs a fixed cost of $7.00 each month for advertising her site. To analyze her financial standing, answer the following:

a. Write an equation representing Angela's monthly Revenue.
b. Formulate an equation illustrating Angela's Monthly Cost.
c. Develop the equation denoting Angela's Monthly Profit Margin.
d. Determine the quantity of bracelets Angela needs to sell each month to achieve a profit.

Moving beyond monthly calculations:

a. Establish an equation representing Angela's yearly Revenue.
b. Craft an equation demonstrating Angela's yearly Cost.
c. Create the equation signifying Angela's yearly Profit Margin.
d. Calculate the number of bracelets Angela must sell each month to ensure a profit over the course of a year.

Answer 1

To find Angela's monthly revenue, multiply the number of bracelets sold by the price of each bracelet. To find her monthly cost, add the fixed cost to the cost of making each bracelet. Subtract the monthly cost from the monthly revenue to find the profit margin. Set the profit margin equation equal to zero to find the quantity of bracelets needed to sell each month to achieve a profit.

Step-by-step explanation:

To find Angela's monthly revenue, we multiply the number of bracelets she sells by the price at which she sells each bracelet. Since Angela sells each bracelet for $2.00 and there is no information given about the quantity of bracelets she sells, we can represent her monthly revenue as R = 2Q, where Q is the quantity of bracelets she sells.

To find Angela's monthly cost, we add her fixed cost of $7.00 for advertising her site to the cost of making each bracelet. Since Angela crafts each bracelet for 65 cents, her Monthly Cost (MC) can be represented as MC = 0.65Q + 7.00.

To determine Angela's monthly profit margin, we subtract her monthly cost from her monthly revenue. So the equation for her Monthly Profit Margin (M) can be represented as M = R - MC = (2Q) - (0.65Q + 7.00).

To find the quantity of bracelets Angela needs to sell each month to achieve a profit, we set the profit margin equation equal to zero and solve for Q. So, (2Q) - (0.65Q + 7.00) = 0. Solving for Q will give us the number of bracelets Angela needs to sell each month to achieve a profit.