To identify which cost item is fixed and variable, we need to understand their behavior with changes in sales volume.
Fixed costs remain constant regardless of the number of units sold. These costs typically include expenses like building rent. In this case, the building rent cost of $9000 is fixed because it does not change with the number of hamburgers sold.
Variable costs, on the other hand, fluctuate directly with the number of units sold. These costs are typically related to the production of goods or services. In this case, the raw materials cost for hamburgers, which is $650, is a variable cost because it changes with the number of units sold.
Next, let's calculate the cost per unit for each item:
Cost per unit of raw materials = Total annual cost of raw materials / Number of units sold
Cost per unit of raw materials = $650 / 1000 = $0.65 per unit
Since the building rent is a fixed cost, the cost per unit remains the same regardless of the number of units sold. Therefore, the cost per unit of building rent is:
Cost per unit of building rent = Total annual cost of building rent / Number of units sold
Cost per unit of building rent = $9000 / 1000 = $9 per unit
Now, let's calculate the total annual cost and unit cost for fixed and variable costs assuming different sales volumes:
For 6000 units sold:
Fixed cost: Building rent remains constant at $9000
Variable cost: Raw materials cost per unit = $0.65
Total annual cost of raw materials for 6000 units = Raw materials cost per unit * Number of units sold = $0.65 * 6000 = $3900
Total annual cost = Fixed cost + Variable cost
Total annual cost = $9000 + $3900 = $12900
Unit cost = Total annual cost / Number of units sold
Unit cost = $12900 / 6000 = $2.15 per unit
For 8000 units sold:
Fixed cost: Building rent remains constant at $9000
Variable cost: Raw materials cost per unit = $0.65
Total annual cost of raw materials for 8000 units = Raw materials cost per unit * Number of units sold = $0.65 * 8000 = $5200
Total annual cost = Fixed cost + Variable cost
Total annual cost = $9000 + $5200 = $14200
Unit cost = Total annual cost / Number of units sold
Unit cost = $14200 / 8000 = $1.775 per unit
In summary:
For 6000 units sold, the total annual cost is $12900, with a unit cost of $2.15 for fixed and variable costs.
For 8000 units sold, the total annual cost is $14200, with a unit cost of $1.775 for fixed and variable costs.