Let's work through this step-by-step using the given data and relevant formulas. --- ## Step 1: Fill in the given data and formulas | Q | TC | FC | VC | MC | ATC | AFC | AFV | AVC | |---|-------|--------|-----|------|--------|--------|--------|--------| | | | | | XXX | XXX | XXX | XXX | XXX | | 1 | | | 3 | | | | | | | 2 | 117 | | | 6 | | | | | | 3 | | | 21 | | | | | | | 4 | | | 21 | | | | | | | 5 | | | | 35.4 | | | | 10.5 | | 6 | | | | 30 | | | 18 | | --- ## Step 2: Calculate Fixed Cost (FC) Fixed Cost (FC) is constant and equals the total fixed cost at any Q. From Q=2, FC is missing, but typically FC remains the same across all quantities. Given FC at Q=2 is not provided directly, but the data indicates that FC is constant. Since no other data points are given, **we'll assume FC at Q=2 is 117** (from Q=2's total cost minus variable costs). --- ## Step 3: Calculate Variable Cost (VC) VC = TC - FC At Q=2: - TC = 117 - FC = 117 (assumed) - VC = 117 - 117 = (which is inconsistent) But from Q=2, VC is not zero; instead, from the table, VC at Q=2 is missing, but VC at Q=1 is 3, and VC at Q=3 is 21. Assuming the total cost at Q=2 is 117, then: VC at Q=2 = TC - FC Since at Q=1: - VC = 3 And at Q=3: - VC = 21 Total cost increases as quantity increases, so perhaps the pattern suggests: - FC is constant across all quantities. - VC at Q=2 is perhaps 6 (since MC at Q=2 is 6). From Q=2: - TC = FC + VC - 117 = FC + VC At Q=1: - VC = 3 - Let's assume FC at Q=1 is TC - VC = 117 - 3 = 114 (which seems inconsistent). Given the data is incomplete, we will proceed with the given variable cost at Q=1 and Q=3: - VC at Q=1 = 3 - VC at Q=2 = 6 - VC at Q=3 = 21 - VC at Q=4 = 21 - VC at Q=6 = 30 --- ## Step 4: Calculate Marginal Cost (MC) Given at Q=2, MC=6 (from the data), and at Q=3, MC=21, etc. --- ## Step 5: Calculate ATC (Average Total Cost) ATC = TC / Q At Q=2: - TC = 117 - ATC = 117 / 2 = **58.5** At Q=6: - TC is not given, but using the pattern: Total cost at Q=6: - TC = FC + VC - FC = 117 (assumed) - VC at Q=6 is 30 (from data) - TC = 117 + 30 = 147 So, ATC at Q=6: - ATC = 147 / 6 = **24.5** --- ## Step 6: Calculate AFC (Average Fixed Cost) AFC = FC / Q Assuming FC = 117: - At Q=6: AFC = 117 / 6 = **19.5** --- ## Step 7: Calculate AVC (Average Variable Cost) AVC = VC / Q At Q=6: - VC = 30 - AVC = 30 / 6 = **5** --- ## **Final Calculations:** ### 1. Total Cost (TC) at P=22 - FC = 117 (assumed constant) - VC at Q=22: Estimate VC per unit: - At Q=6, VC=30 → VC per unit ≈ 30/6=5 - Assuming VC increases linearly, at Q=22: VC ≈ 5 * 22 = 110 Total Cost: - TC = FC + VC = 117 + 110 = **227** --- ### 2. Profit Profit = Revenue - Total Cost Revenue = P * Q = 22 * 22 = 484 Profit = 484 - 227 = **257** --- # **Final Answers** - **Number of units to produce (Q):** 22 units - **Profit:** **257** --- **Note:** Due to incomplete data, some assumptions were made, especially regarding FC. The approach relies on typical cost relationships and the given data points.