Question

The company is going to begin selling these through Amazon.com. In order to keep their profits at an acceptable level, they must keep their average cost per headset below $50. The average cost per headset can be calculated using the formula: 25x+50000/x≤50 where x represents the number of headsets that are manufactured each month. A) What are the range of headsets to be manufactured that will keep these costs at the needed level? B) Amazon.com predicts that they can expect an initial sales month of 5,000 units. After the initial month, the prediction is for 2025 units each month. With the predicted sales, will the company be able to adequately sustain their costs below $50 per unit while meeting the demand?

Answer 1

Part A:

Given that the average cost per headset can be calculated by the formular:


`(25x+50000)/(x) \leq50`

The range of headsets to be manufactured that will keep these costs at the needed level is given by the solution to the inequality above given as follows:


`25x+50000\leq50x \\ \\ \Rightarrow25x-50x\leq-50000 \\ \\ \Rightarrow-25x\leq-50000 \\ \\ \Rightarrow x\leq(-50000)/(-25) \\ \\ \Rightarrow x\leq2,000`

Therefore, to keep the costs at the needed level, the company should produce 2000 or less headsets.



Part B:

From part A we have that the number of headsets the company should produce in other to keep the costs at the required level is 2000 units or less.

Therefore, given that they can expect an initial sales month of 5,000 units. After the initial month, the prediction is for 2025 units each month.

This means with the required cost levels the company will not be able to adequately maintain demand while sustaining their cost below $50 per unit.