Break Even – Fixed and Variable Expenses

Student WorksheetName:______

FIXED AND VARIABLE EXPENSES

You want to open an ice cream parlor/store.

  1. Based on the previous discussion, is this business likely to have higher fixed costs or variable costs? Why?
  1. What are some of the fixed expenses associated with this business?
  1. What are some of the variable expenses associated with this business?
  1. If one person comes in to buy ice cream or 100 people come in to buy ice cream, how does this affect your expenses in general?
  1. What would be some of your initial, or start-up costs?

You have determined that the expenses for this business are as follows:

Fixed Expenses / Monthly Cost / Variable Expenses / Cost per sale/each
Store rental / $930 / Ice cream / $0.50
Utilities / $400 / Cones/Cups / $0.15
Payroll: 2 employees - $8.50/hour – 40 hours per week / $2,720 / Spoons / $0.05
Insurance / $100 / Toppings / $0.13
Advertising/Marketing / $100 / Napkins / $0.02
Total / $4,250.00 / Total / $0.85
  1. Each ice cream that you sell comes with a fixed portion of ice cream, a cup or cone, a spoon, a topping of choice, and a napkin. Explain the cost per sale/each.
  1. Write an equation that models your monthly expenses as a function of the number of ice cream you sell, incorporating both your fixed and variable expenses. Let y = total monthly expenses ($) and x = # of ice creams you sell per month.
  1. As the number of ice creams you sell per month increases, how does this affect your monthly expenses?
  1. You decide to sell your product for $3.35. Write an equation that models your total monthly revenues as a function of the number of ice creams you sell. Let y = total monthly revenues ($) and x = # of ice creams you sell per month.
  1. As the number of ice creams you sell per month increases, how does this affect your monthly revenues?
  1. What is the starting point of the monthly expenses (when you have sold 0 ice creams)?
  1. What is the starting point of your monthly revenues (when you have sold 0 ice creams)?
  1. Which increases at a faster rate, your expenses or revenues? How do you know?
  1. How many ice creams do you need to sell each month to break even? (When do the lines meet?) Solve this numerically.
  1. If you are open 7 days a week for a total of 40 hours per week (and there are approximately 4 weeks per month), approximately how many ice creams is this per day?
  1. Your initial investment costs for this business including the freezers, scoops, cash register, and signage totaled $7,000. If you believe that you can sell 2,100 ice creams per month for $3.50 each, estimate how long it will take you to break even accounting for this initial investment.
  1. What are your monthly revenues now?
  1. Write an equation that models cumulative total revenues as a function of the time (in months). Let y = revenues ($) and x = # of months.
  1. Write an equation that models cumulative total expenses, accounting for both initial and fixed expenses, as a function of time (in months). Let y = expenses ($) and x = # of months.
  1. At what point do these lines meet? Solve this numerically and graphically.

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