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.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

Quizplus · Accepted Answer

To minimize AVC, set its derivative equal to zero and solve for Q:$$\frac{dAVC}{dQ} = -0.026 + 0.000006Q = 0$$$$0.000006Q = 0.026$$$$Q = 4333.33$$Then, plug Q back into the AVC function to find the minimum AVC:$$AVC = 88 - 0.026 (4333.33) + 0.000003 (4333.33)^2 = 23.33$$Finally, use the definition of AVC to find TVC:$$TVC = AVC 	imes Q = 23.33 	imes 4333.33 = 101,101$$

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 $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$