The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.At what level of output does average variable cost (AVC)reach its minimum value for Greene Enterprises?
A)800
B)3,144
C)3,800
D)4,333
E)51,672

Question

Quizplus · Accepted Answer

To find the minimum AVC, we need to find the derivative of AVC with respect to Q and set it equal to 0:
AVC' = -0.026 + 0.000006Q = 0
0.000006Q = 0.026
Q = 4,333.33
Since this is the only choice that is close to 4,333, it is the correct answer.

The Manager of Greene Enterprises,Inc AVC=88−0.026Q+0.000003Q2A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }AVC=88−0.026Q+0.000003Q2

The Manager of Greene Enterprises,Inc $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$