Average cost = q^2¡V15q + 48
Calculate the output level (q), which minimizes
a)Total Cost
b)Marginal Cost
I got an answer for a) is q=8 and b) is q=5
I need somebody to check it for me, thanks so much.
To find the output level (q) that minimizes the total cost, you need to find the minimum point of the cost function. This can be done by taking the derivative of the cost function with respect to q and setting it equal to zero. Then solve for q.
a) Total Cost:
The cost function is given as: Average cost = q^2 - 15q + 48.
To minimize the total cost, we need to find the minimum point of the cost function.
1. Take the derivative of the cost function with respect to q:
d/dq [q^2 - 15q + 48] = 2q - 15.
2. Set the derivative equal to zero and solve for q:
2q - 15 = 0
2q = 15
q = 15/2
q = 7.5
Therefore, the output level (q) that minimizes the total cost is q = 7.5.
b) Marginal Cost:
To minimize the marginal cost, you need to find the output level where the derivative of the cost function with respect to q is equal to zero.
1. Take the derivative of the cost function with respect to q:
d/dq [q^2 - 15q + 48] = 2q - 15.
2. Set the derivative equal to zero and solve for q:
2q - 15 = 0
2q = 15
q = 15/2
q = 7.5
Therefore, the output level (q) that minimizes the marginal cost is q = 7.5.
It seems there might be an error in the calculation you provided. The correct answer for both a) and b) is q = 7.5, not q = 8 and q = 5.