The per-unit cost of the application

  To find the per-unit cost of the application, we need to calculate the average total cost (ATC) for different quantities sold. The average total cost is defined as: [ \text{Average Total Cost (ATC)} = \frac{\text{Total Cost}}{\text{Quantity Sold}} ] Step 1: Determine Total Cost The total cost consists of two components: 1. Fixed Costs: This is the initial development cost of the application, which is $100,000. 2. Variable Costs: This is the cost incurred for each unit delivered, which is $0.50 per unit. The total cost can be calculated as follows: [ \text{Total Cost} = \text{Fixed Costs} + (\text{Variable Cost per Unit} \times \text{Quantity Sold}) ] Step 2: Calculate Total Cost for Different Quantities 1. For 100 Units: - Fixed Costs: $100,000 - Variable Costs: (0.50 \times 100 = 50) [ \text{Total Cost} = 100,000 + 50 = 100,050 ] Now, let's calculate the ATC: [ \text{ATC} = \frac{100,050}{100} = 1,000.50 ] 2. For 1,000 Units: - Fixed Costs: $100,000 - Variable Costs: (0.50 \times 1,000 = 500) [ \text{Total Cost} = 100,000 + 500 = 100,500 ] Now, let's calculate the ATC: [ \text{ATC} = \frac{100,500}{1,000} = 100.50 ] 3. For 1,000,000 Units: - Fixed Costs: $100,000 - Variable Costs: (0.50 \times 1,000,000 = 500,000) [ \text{Total Cost} = 100,000 + 500,000 = 600,000 ] Now, let's calculate the ATC: [ \text{ATC} = \frac{600,000}{1,000,000} = 0.60 ] Summary of Results - Per-Unit Cost for 100 Units: $1,000.50 - Per-Unit Cost for 1,000 Units: $100.50 - Per-Unit Cost for 1,000,000 Units: $0.60 Explanation of Results As demonstrated in the calculations: - The per-unit cost is significantly higher when selling a smaller quantity (e.g., 100 units) due to the fixed costs being spread over a smaller number of units. - As the quantity sold increases (to 1,000 and then to 1 million units), the fixed costs get distributed over a larger number of units, causing the average total cost per unit to decrease. - This illustrates the principle of economies of scale in production and delivery: as more units are produced and sold, the average cost per unit declines due to the fixed costs being spread out over more units.

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