Answer:
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
Answer:
69
Step-by-step explanation:
All the given arcs cover the entire circle circumference, so their measures add up to a full 360.
(2x - 16) + (x + 40) + x + 60 = 360
4x + 84 = 360
4x = 276
x = 69
Answer:
2,500 German chocolate cake boxes.
1,500 Swiss chocolate cake boxes.
Step-by-step explanation:
Let 'S' be the number of Swiss chocolate cakes boxed and 'G' the number of German cholocate cakes boxed. If all of the available ingredients are used:
Solving the linear system above:
2,500 German chocolate cake boxes and 1,500 Swiss chocolate cake boxes can be made each day.
