Using the provided graph and formulas, calculate the firm's variable cost at output levels 2, 4, and 6, and its average total cost at output levels 5 and 7.

$$\text{TVC} = \text{TC} - \text{TFC}$$

• At Q = 2: $$\text{TVC}(2) = \text{TC}(2) - \text{TFC} = 35 - 20 = 15$$
• At Q = 4: $$\text{TVC}(4) = \text{TC}(4) - \text{TFC} = 50 - 20 = 30$$
• At Q = 6: $$\text{TVC}(6) = \text{TC}(6) - \text{TFC} = 85 - 20 = 65$$
• i) Variable Cost at output levels 2, 4, 6:
  • Q=2: \boxed{\text{\15}}$
  • Q=4: \boxed{\text{\30}}$
  • Q=6: \boxed{\text{\65}}$

$$\text{ATC} = \frac{\text{TC}}{\text{Q}}$$

• At Q = 5: $$\text{ATC}(5) = \frac{\text{TC}(5)}{5} = \frac{65}{5} = 13$$
• At Q = 7: $$\text{ATC}(7) = \frac{\text{TC}(7)}{7} = \frac{110}{7} \approx 15.71$$
• ii) Average Cost at output levels 5 and 7:
  • Q=5: \boxed{\text{\13}}$
  • Q=7: \boxed{\text{\15.71}}$

$$\text{MC} = \text{TC}(\text{Q}) - \text{TC}(\text{Q}-1)$$

• At Q = 4: $$\text{MC}(4) = \text{TC}(4) - \text{TC}(3) = 50 - 40 = 10$$
• At Q = 6: $$\text{MC}(6) = \text{TC}(6) - \text{TC}(5) = 85 - 65 = 20$$
• iii) Marginal Cost at output levels 4 and 6:
  • Q=4: \boxed{\text{\10}}$
  • Q=6: \boxed{\text{\20}}$

Given Price (P) = $40.

$$\text{TR}(3) = \text{P} \times \text{Q} = 40 \times 3 = 120$$

From the graph, TC(3) = 40.

$$\text{Profit}(3) = \text{TR}(3) - \text{TC}(3) = 120 - 40 = 80$$

• i) Profit at 3 units: \boxed{\text{\80}}$

$$\text{TR}(5) = \text{P} \times \text{Q} = 40 \times 5 = 200$$

From the graph, TC(5) = 65.

$$\text{Profit}(5) = \text{TR}(5) - \text{TC}(5) = 200 - 65 = 135$$

• ii) Profit at 5 units: \boxed{\text{\135}}$

$$\text{TR}(7) = \text{P} \times \text{Q} = 40 \times 7 = 280$$

From the graph, TC(7) = 110.

$$\text{Profit}(7) = \text{TR}(7) - \text{TC}(7) = 280 - 110 = 170$$

• iii) Profit at 7 units: \boxed{\text{\170}}$