To determine the profit for each quantity level provided in the table, we need to follow a systematic calculation. Profit is defined as the difference between total revenue and total cost. Here's the step-by-step solution:
1. Calculate Total Revenue:
- For each quantity level, the total revenue is calculated by multiplying the quantity by the price per unit.
2. Calculate Profit:
- The profit for each quantity level is the difference between the total revenue and the total cost.
Let's break down the calculations for each quantity level:
1. Quantity: 10
- Price per Unit: \$100
- Total Cost: \$100
- Total Revenue = Quantity × Price per Unit = 10 × \[tex]$100 = \$[/tex]1,000
- Profit = Total Revenue - Total Cost = \[tex]$1,000 - \$[/tex]100 = \$900
2. Quantity: 20
- Price per Unit: \$80
- Total Cost: \$400
- Total Revenue = Quantity × Price per Unit = 20 × \[tex]$80 = \$[/tex]1,600
- Profit = Total Revenue - Total Cost = \[tex]$1,600 - \$[/tex]400 = \$1,200
3. Quantity: 30
- Price per Unit: \$60
- Total Cost: \$800
- Total Revenue = Quantity × Price per Unit = 30 × \[tex]$60 = \$[/tex]1,800
- Profit = Total Revenue - Total Cost = \[tex]$1,800 - \$[/tex]800 = \$1,000
4. Quantity: 40
- Price per Unit: \$40
- Total Cost: \$1,400
- Total Revenue = Quantity × Price per Unit = 40 × \[tex]$40 = \$[/tex]1,600
- Profit = Total Revenue - Total Cost = \[tex]$1,600 - \$[/tex]1,400 = \$200
5. Quantity: 50
- Price per Unit: \$20
- Total Cost: \$2,400
- Total Revenue = Quantity × Price per Unit = 50 × \[tex]$20 = \$[/tex]1,000
- Profit = Total Revenue - Total Cost = \[tex]$1,000 - \$[/tex]2,400 = -\$1,400
Summarizing the profits for each quantity level, we have:
- For Quantity 10: \$900
- For Quantity 20: \$1,200
- For Quantity 30: \$1,000
- For Quantity 40: \$200
- For Quantity 50: -\$1,400
The completion of these steps yields the profit values:
[tex]\[ [\[tex]$900, \$[/tex]1,200, \[tex]$1,000, \$[/tex]200, -\$1,400] \][/tex]
From the options provided, the relevant value that matches one of the calculated profits is \$1,200.
