7.Your cousin Vinnie owns a painting company with fixed costs of $200 and the following schedule for variable costs:

Quantity of Houses Painted per
Month 1 2 3 4 5 6 7

Variable Costs $10 $20 $40 $80 $160 $320 $640
Calculate average fixed cost, average variable cost, and average total cost for each quantity. What is the efficient scale of the painting company?

To calculate the average fixed cost, average variable cost, and average total cost, we need to use the following formulas:

Average Fixed Cost = Total Fixed Cost / Quantity
Average Variable Cost = Total Variable Cost / Quantity
Average Total Cost = Average Fixed Cost + Average Variable Cost

Let's calculate these values for each quantity:

For Quantity 1:
Average Fixed Cost = $200 / 1 = $200
Average Variable Cost = $10 / 1 = $10
Average Total Cost = $200 + $10 = $210

For Quantity 2:
Average Fixed Cost = $200 / 2 = $100
Average Variable Cost = $20 / 2 = $10
Average Total Cost = $100 + $10 = $110

For Quantity 3:
Average Fixed Cost = $200 / 3 = $66.67 (rounded to two decimal places)
Average Variable Cost = $40 / 3 = $13.33 (rounded to two decimal places)
Average Total Cost = $66.67 + $13.33 = $80

For Quantity 4:
Average Fixed Cost = $200 / 4 = $50
Average Variable Cost = $80 / 4 = $20
Average Total Cost = $50 + $20 = $70

For Quantity 5:
Average Fixed Cost = $200 / 5 = $40
Average Variable Cost = $160 / 5 = $32
Average Total Cost = $40 + $32 = $72

For Quantity 6:
Average Fixed Cost = $200 / 6 = $33.33 (rounded to two decimal places)
Average Variable Cost = $320 / 6 = $53.33 (rounded to two decimal places)
Average Total Cost = $33.33 + $53.33 = $86.67 (rounded to two decimal places)

For Quantity 7:
Average Fixed Cost = $200 / 7 = $28.57 (rounded to two decimal places)
Average Variable Cost = $640 / 7 = $91.43 (rounded to two decimal places)
Average Total Cost = $28.57 + $91.43 = $120 (rounded to two decimal places)

To find the efficient scale of the painting company, we look for the quantity at which the average total cost is minimized. In this case, the efficient scale is at Quantity 4, where the average total cost is $70. This means that producing 4 houses per month is the most efficient level for the company.