Suppose the total cost in naira in manufacturing q unit of commodity is C =3q²+7q + 15
Derive a formular for marginal cost
What is the marginal cost when 60 units have been produced
What is the actual cost of producing 61 units
To derive the formula for marginal cost, we need to find the derivative of the cost function with respect to the quantity (q). The derivative of a polynomial follows the power rule, where the exponent in each term is multiplied by the coefficient and then reduced by one.
Given the cost function C = 3q² + 7q + 15, let's find the derivative:
dC/dq = d(3q²)/dq + d(7q)/dq + d(15)/dq
Applying the power rule:
dC/dq = 2 * 3 q^(2-1) + 1 * 7 q^(1-1) + 0
dC/dq = 6q + 7
Therefore, the formula for the marginal cost (MC) is:
MC = 6q + 7
To find the marginal cost when 60 units have been produced, we substitute q = 60 into the derived formula:
MC = 6(60) + 7
MC = 360 + 7
MC = 367 naira
So, the marginal cost when 60 units have been produced is 367 naira.
To find the actual cost of producing 61 units, we substitute q = 61 into the original cost function:
C = 3(61)² + 7(61) + 15
C = 3(3721) + 427 + 15
C = 11163 + 427 + 15
C = 11605 naira
Therefore, the actual cost of producing 61 units is 11605 naira.