Provide an appropriate response.
-The total cost in dollars of producing x lawn mowers is given by C Find the marginal average cost at and interpret the result.
A) -$13.33; a unit increase in production will decrease the average cost per unit by approximately $13.33 at a production level of 20 units.
B) -$1.33; a unit increase in production will decrease the average cost per unit by approximately $1.33 at a production level of 20 units.
C) -$10.33; a unit increase in production will decrease the average cost per unit by approximately $10.33 at a production level of 20 units.
D) -$20.33; a unit increase in production will decrease the average cost per unit by approximately $20.33 at a production level of 20 units.

Question

Provide an appropriate response.
-The total cost in dollars of producing x lawn mowers is given by C  Find the marginal average cost at  and interpret the result.
A) -$13.33; a unit increase in production will decrease the average cost per unit by approximately $13.33 at a production level of 20 units. 
B) -$1.33; a unit increase in production will decrease the average cost per unit by approximately $1.33 at a production level of 20 units. 
C) -$10.33; a unit increase in production will decrease the average cost per unit by approximately $10.33 at a production level of 20 units. 
D) -$20.33; a unit increase in production will decrease the average cost per unit by approximately $20.33 at a production level of 20 units.

Quizplus · Accepted Answer

To find the marginal average cost, we need to find the derivative of the cost function with respect to x, and then evaluate it at x=20. The derivative of the function is -10x^(-2/3), and plugging in x=20 gives us a value of approximately -10.33. This means that a unit increase in production (from 20 to 21) will decrease the average cost per unit by approximately $10.33. To find the marginal average cost, we need to take the derivative of the cost function and evaluate it at a production level of 20 units. The derivative of the given cost function is 33x^2-264x+481, and evaluating it at x=20 gives a marginal average cost of approximately -$10.33. The negative sign means that the cost is decreasing as production increases, and the value of $10.33 tells us the amount by which the average cost is decreasing for each additional unit produced.

Provide an Appropriate Response