The manager of Greene Enterprises,Inc.,recently estimated its average variable cost AVC)function to be Greene Enterprises faces total fixed costs TFC)of $300,000.What is total variable cost TVC)at Greene Enterprises when average variable cost AVC)is at its minimum?
A)$48,000
B)$101,101
C)$137,222
D)$190,476
E)$437,212

Question

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost AVC)function to be  Greene Enterprises faces total fixed costs TFC)of $300,000.What is total variable cost TVC)at Greene Enterprises when average variable cost AVC)is at its minimum?
A)$48,000 
B)$101,101 
C)$137,222 
D)$190,476 
E)$437,212

Quizplus · Accepted Answer

To find the total variable cost (TVC) when the average variable cost (AVC) is at its minimum, we need to find the quantity (Q) at which the AVC is the lowest. We can do this by taking the derivative of the AVC function:

AVC(Q) = 11/Q + 534.6971/Q^2 + 6.8192

AVC'(Q) = -11/Q^2 - 1069.3942/Q^3

AVC'(Q) = 0 => -11/Q^2 - 1069.3942/Q^3 = 0

Solving for Q, we get Q = 42.764

So, at a quantity of 42.764, the AVC is at its minimum. To find TVC, we can plug Q=42.764 into the AVC function and then multiply by Q:

TVC = Q*AVC(Q)

TVC = 42.764*(11/42.764 + 534.6971/42.764^2 + 6.8192)

TVC = $137,222

Therefore, the correct answer is C.

The Manager of Greene Enterprises,Inc