To determine the Total Fixed Cost (TFC), we need to identify the component of the cost function that represents fixed costs.
In the given cost function, C = 0.05Q^2 + 0.1Q + 20, the constant term 20 represents the fixed costs. Therefore, TFC = $20.
To determine the Total Variable Cost (TVC), we can subtract the fixed cost from the total cost:
TVC = C - TFC = 0.05Q^2 + 0.1Q + 20 - 20 = 0.05Q^2 + 0.1Q.
To find the Average Total Cost (ATC) of producing 6 units, we divide the total cost by the quantity:
ATC = C/Q = (0.05Q^2 + 0.1Q + 20)/Q = 0.05Q + 0.1 + 20/Q.
Substituting Q = 6, we find:
ATC(6) = 0.05(6) + 0.1 + 20/6 = 0.3 + 0.1 + 20/6 ≈ 0.5 + 3.333 ≈ 3.833.
To find the Marginal Cost (MC) of the 6th unit, we take the derivative of the cost function with respect to quantity (Q) and evaluate it at Q = 6:
MC = dC/dQ = 0.1Q + 0.1.
Substituting Q = 6, we find:
MC(6) = 0.1(6) + 0.1 = 0.6 + 0.1 = 0.7.
Suppose a cost function is given as . C= 0.05Q^2+.0.1Q+20
Determine:
A. TFC
. TVC and ATC of producing 6 units
. MC of the 6th unit
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