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

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

pls mark as brainliest

the photograph is photographer and- in the process- ourselves.

step-by-step explanation: