Marginal cost At a certain factory the marginal cost is 3 (q-4) ^2 dollars per unit when the level of production is q units.

a.) Express the total production cost in terms of overhead (the cost of production 0

units) and the number of units produced.

b.) what is the cost of producing 14 units if the overhead $436?

a.) C (q) = - (1/4) * q^3 + 3q^2 - 12q + OH b.) $170

Step-by-step explanation:

(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:

Marginal cost (MC) = change in total cost/change in quantity

Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:

Total cost (C) = Integral [3 (q-4) ^2] dq = - (1/4) * (q-4) ^3 + k

where k is a constant.

The overhead (OH) = C (0) = - (1/4) * (0-4) ^3 + k = - 16 + k

C (q) = - (1/4) * (q^3 - 12q^2 + 48q - 64) + k = - (1/4) * q^3 + 3q^2 - 12q - 16 + k

Thus:

C (q) = - (1/4) * q^3 + 3q^2 - 12q + OH

(b) C (14) = - (1/4) * 14^3 + 3*14^2 - 12*14 + 436 = - 686 + 588 - 168 + 436 = $170