Question

The average cost per item, C, of manufacturing a quantity q of cell phones is given by C = (a/q) +b. Find the rate of change of C as q increases. if production increases at a rate of 100 cell phones per week, how fast is the average cost changing?

Answer 1

Answer: The average cost per item is given by the equation C = (a/q) + b. To find the rate of change of C as q increases, we need to take the derivative of this equation with respect to q.

dC/dq = -(a/q^2)

So, the rate of change of C with respect to q is proportional to -1/q^2.

If production increases at a rate of 100 cell phones per week, the rate of change of q is 100. But we need to convert this to units of items per hour or per second, depending on the context.

Let's assume the rate of increase of q is in items per hour. Then the rate of change of C with respect to time t (in hours) is given by:

dC/dt = (dC/dq) * (dq/dt) = (-(a/q^2)) * (100) = -100a/q^2

So, the rate at which the average cost is changing depends on the value of a and q. If we knew the values of a and q, we could calculate the specific rate at which the average cost is changing.

Explanation: