John is considering adding balloons to the product line he sells at the shop. There will be a cost of $200.00 for leasing the necessary equipment. The cost of buying balloons and helium and paying a worker is expected to be $4.25 per unit (balloon). He expects to sell the balloons for $6.75 each. a) Write the total cost function. b) Write the variable cost function. c) Write the revenue function. d) If John sells 70 balloons, calculate: average fixed cost, variable cost, revenue, average total cost. e) Will there be a profit or loss at this level of sales? How much? f) Determine the breakeven number of balloons.

Question

John is considering adding balloons to the product line he sells at the shop. There will be a cost of $200.00 for leasing the necessary equipment. The cost of buying balloons and helium and paying a worker is expected to be $4.25 per unit (balloon). He expects to sell the balloons for $6.75 each. a) Write the total cost function. b) Write the variable cost function. c) Write the revenue function. d) If John sells 70 balloons, calculate: average fixed cost, variable cost, revenue, average total cost. e) Will there be a profit or loss at this level of sales? How much? f) Determine the breakeven number of balloons.

Answer 1

a) The total cost function can be calculated by summing up the fixed cost (leasing equipment) and the variable cost (balloons, helium, and worker cost) multiplied by the number of units (balloons).

Total Cost Function = Fixed Cost + (Variable Cost per unit * Number of units)

Fixed Cost = $200.00
Variable Cost per unit = $4.25

So, the total cost function is:
Total Cost = $200.00 + ($4.25 * Number of Units)

b) The variable cost function represents only the cost directly related to producing each unit (balloon). It can be calculated as:

Variable Cost Function = Variable Cost per unit * Number of units

Variable Cost per unit = $4.25

So, the variable cost function is:
Variable Cost = $4.25 * Number of Units

c) The revenue function represents the total revenue generated from selling the units (balloons). It can be calculated as:

Revenue Function = Selling Price per unit * Number of units

Selling Price per unit = $6.75

So, the revenue function is:
Revenue = $6.75 * Number of Units

d) If John sells 70 balloons:
- Average Fixed Cost = Total Fixed Cost / Number of Units
- Variable Cost = Variable Cost per unit * Number of Units
- Revenue = Selling Price per unit * Number of Units
- Average Total Cost = Total Cost / Number of Units

Using the given information:
Fixed Cost = $200.00
Variable Cost per unit = $4.25
Selling Price per unit = $6.75
Number of Units = 70

Average Fixed Cost = $200.00 / 70
Variable Cost = $4.25 * 70
Revenue = $6.75 * 70
Average Total Cost = (Fixed Cost + Variable Cost) / 70

Calculate these values using the above formulas.

e) To determine if there will be a profit or loss, we need to compare the revenue with the total cost. If the revenue is higher than the total cost, there will be a profit. If the total cost is higher than the revenue, there will be a loss.

Profit/Loss = Revenue - Total Cost

Substitute the values of Revenue and Total Cost calculated in part d, and calculate the profit or loss.

f) The break-even point is the level of sales where the revenue equals the total cost, resulting in neither a profit nor a loss.

To calculate the break-even point, we need to set the revenue equal to the total cost and then solve for the number of units (balloons).

Revenue = Total Cost

Substitute the Revenue and Total Cost functions calculated earlier, and solve for the number of units (balloons).