Minimizing Average Cost Functions

The video tutorial explains how to analyze a cost function, C(x) = 62,500 + 500x + x^2, to determine various cost metrics at a production level of 1050. It covers calculating the total cost, average cost, and marginal cost. The tutorial also demonstrates how to find the production level that minimizes the average cost using calculus, and calculates the minimum average cost at this optimal level.

What is the formula for the given cost function?

• c(x) = 70,000 + 600x + x^2

• c(x) = 50,000 + 400x + x^2

• c(x) = 60,000 + 500x + x^3

• c(x) = 62,500 + 500x + x^2

What is the total cost at a production level of 1050?

• $1,700,000

• $1,600,000

• $1,690,000

• $1,500,000

How is the average cost function derived from the total cost function?

• By multiplying the total cost by the production level

• By dividing the total cost by the production level

• By adding a constant to the total cost

• By subtracting a constant from the total cost

What is the average cost at a production level of 1050?

• $1,500.00

• $1,700.00

• $1,800.00

• $1,609.52

What is the marginal cost function derived from?

• The integral of the cost function

• The derivative of the cost function

• The average of the cost function

• The sum of the cost function

What is the marginal cost at a production level of 1050?

• $2,700

• $2,800

• $2,600

• $2,500

What method is used to find the production level that minimizes the average cost?

• Second derivative test

• Integration

• Substitution

• First derivative test

What is the production level that minimizes the average cost?

• 200

• 350

• 250

• 300

What is the minimum average cost per item?

• $1,000

• $1,100

• $1,200

• $1,300

What is the significance of the second derivative being positive at the critical point?

• The function is constant, indicating no change

• The function is linear, indicating no extremum

• The function is concave up, indicating a minimum

• The function is concave down, indicating a maximum