Question

The average cost per item to produce q items is given by a(q)=0.04q²−1.2q+15 What is the total cost, C(q), of producing q goods?

What is the minimum marginal cost?
At what production level is the average cost a minimum?
What is the lowest average cost?
Compute the marainal cost at a=15. MC(15)=

Answer 1

To find the total cost, multiply the average cost per item by the quantity of items produced. The minimum marginal cost is found by setting the derivative of the cost function equal to 0. The lowest average cost is obtained by finding the vertex of the quadratic function.

Step-by-step explanation:

The total cost, C(q), of producing q goods can be calculated by multiplying the average cost per item, a(q), by the quantity of items produced, q. So, the formula for total cost is C(q) = q * a(q).

To find the minimum marginal cost, we need to find the derivative of the cost function C(q) with respect to q and set it equal to 0. The value of q at which this occurs will give us the production level at which the average cost is a minimum.

The lowest average cost is obtained by finding the value of q that minimizes the average cost function a(q). This can be done by finding the vertex or maximum/minimum point of the quadratic function.

To compute the marginal cost at a production level of 15 (a=15), plug in the value of q into the derivative of the cost function.