To determine the optimal number of units to produce in order to maximize profit, we need to assess the profit at each level of total output. Profit can be calculated by subtracting the total cost from the total revenue at each output level. Let's go through the calculations step by step:
1. Calculate the profit for each output level:
- For 0 units: \[tex]$0 (revenue) - \$[/tex]1,000 (cost) = -\[tex]$1,000 (profit)
- For 1 unit: \$[/tex]1,700 (revenue) - \[tex]$2,000 (cost) = -\$[/tex]300 (profit)
- For 2 units: \[tex]$3,300 (revenue) - \$[/tex]2,800 (cost) = \[tex]$500 (profit)
- For 3 units: \$[/tex]4,800 (revenue) - \[tex]$3,500 (cost) = \$[/tex]1,300 (profit)
- For 4 units: \[tex]$6,200 (revenue) - \$[/tex]4,000 (cost) = \[tex]$2,200 (profit)
- For 5 units: \$[/tex]7,500 (revenue) - \[tex]$4,500 (cost) = \$[/tex]3,000 (profit)
- For 6 units: \[tex]$8,500 (revenue) - \$[/tex]5,500 (cost) = \[tex]$3,000 (profit)
- For 7 units: \$[/tex]9,000 (revenue) - \[tex]$6,500 (cost) = \$[/tex]2,500 (profit)
- For 8 units: \[tex]$10,800 (revenue) - \$[/tex]8,000 (cost) = \[tex]$2,800 (profit)
- For 9 units: \$[/tex]11,700 (revenue) - \[tex]$12,000 (cost) = -\$[/tex]300 (profit)
2. Summarize the profit for each output level:
- 0 units: -\[tex]$1,000
- 1 unit: -\$[/tex]300
- 2 units: \[tex]$500
- 3 units: \$[/tex]1,300
- 4 units: \[tex]$2,200
- 5 units: \$[/tex]3,000
- 6 units: \[tex]$3,000
- 7 units: \$[/tex]2,500
- 8 units: \[tex]$2,800
- 9 units: -\$[/tex]300
3. Find the maximum profit and the corresponding output level:
- The maximum profit is \$3,000, which occurs at both 5 and 6 units of output.
Therefore, in order to maximize profits, the firm should produce 5 units of output.
