Given the following for perfectly competitive firm that has short-run cost structure

Output Marginal Cost
1 $10
2 $5
3 $12
4 $23
5 $40

Total fixed costs are $20 and the market price of the product is $25 per unit. How much output should the profit-maximizing firm produce (if any) and how much profit or loss will the firm make in the short run?

please show me example of the question above thank you

To determine the profit-maximizing level of output for a perfectly competitive firm in the short run, we need to compare the market price of the product with the firm's marginal cost.

1. Sort the given data in ascending order based on the level of output:
Output | Marginal Cost
1 | $10
2 | $5
3 | $12
4 | $23
5 | $40

2. Since this is a perfectly competitive market, the firm is a price taker, meaning it has no control over the market price. The given market price is $25.

3. Calculate the total variable cost (TVC) by adding up the marginal costs for the level of output:
TVC = $10 + $5 + $12 + $23 + $40 = $90

4. Calculate the total cost (TC) by adding the total fixed costs (TFC) to the TVC:
TFC = $20
TC = TFC + TVC
= $20 + $90
= $110

5. To determine the profit or loss, subtract the total cost from the total revenue:
Total revenue (TR) = Price per unit * Quantity
= $25 * Quantity

6. Set up the profit equation:
Profit = TR - TC

7. Now, we can analyze the profit-maximizing level of output:
- If the market price is higher than the marginal cost (P > MC), the firm should produce more to increase its profit.
- If the market price is lower than the marginal cost (P < MC), the firm should reduce its output to minimize its loss.
- If the market price is equal to the marginal cost (P = MC), the firm is at its profit-maximizing level of output.

Let's calculate the profit at each level of output and determine the profit-maximizing level:

For output level 1:
TR = $25 * 1 = $25
Profit = TR - TC
= $25 - $110
= -$85 (loss)

For output level 2:
TR = $25 * 2 = $50
Profit = TR - TC
= $50 - $110
= -$60 (loss)

For output level 3:
TR = $25 * 3 = $75
Profit = TR - TC
= $75 - $110
= -$35 (loss)

For output level 4:
TR = $25 * 4 = $100
Profit = TR - TC
= $100 - $110
= -$10 (loss)

For output level 5:
TR = $25 * 5 = $125
Profit = TR - TC
= $125 - $110
= $15 (profit)

From the above calculations, we can see that the firm should produce an output level of 5 in the short run in order to maximize its profit. At this level, the firm will make a profit of $15.

It is important to note that in the short run, a perfectly competitive firm will continue to operate even if it incurs a loss as long as it can cover its variable costs.