A firm's total cost furniture is given as:
TC = q³ (10 + 5q²)
Find the marginal cost function.
To find the marginal cost function, we first need to find the total cost function.
Given:
TC = q³ (10 + 5q²)
To find the marginal cost, we need to find the derivative of the total cost function with respect to quantity (q).
Let's find the derivative of TC with respect to q:
dTC/dq = d/dq [q³ (10 + 5q²)]
dTC/dq = 3q² (10 + 5q²) + q³ (0 + 10q)
dTC/dq = 30q² + 15q⁴
Therefore, the marginal cost function (MC) is the derivative of the total cost function with respect to quantity (q):
MC = dTC/dq
MC = 30q² + 15q⁴
Hence, the marginal cost function is:
MC = 30q² + 15q⁴.