Final answer:
There is no value of Q at which the average cost is minimized for this cost function.
Step-by-step explanation:
In order to find the value of Q at which average cost is minimized, we need to differentiate the cost function with respect to Q and set it equal to zero.
The average cost can be derived from the cost function by dividing C(Q) by Q. So, we have:
AC(Q) = (60 + 2Q + 0.05Q^2) / Q
To find the minimum, we differentiate AC(Q) with respect to Q:
d(AC(Q))/dQ = (2 + 0.1Q - 1) / Q^2 = 0
Setting the derivative equal to zero and solving for Q:
2 + 0.1Q - 1 = 0
0.1Q = -1
Q = -10
However, since we are dealing with quantities, a negative value for Q does not make sense in this context.
Therefore, there is no value of Q at which average cost is minimized for this cost function.