Q:

In the cost function below, C(x) is the cost of producing x items. Find the average cost per item when the required number of items is produced C(x)=7.6x + 10,800 a 200 items b. 2000 items c. 5000 items a. What is the average cost per item when 200 items are produced?

Accepted Solution

A:
Answer:Given :Cost function : [tex]C(x)=7.6x + 10,800[/tex]To Find : Find the average cost per item when the required number of items is producedSolution:a) 200 items Cost function : [tex]C(x)=7.6x + 10,800[/tex]Substitute x = 200 [tex]C(200)=7.6(200)+ 10,800[/tex][tex]C(200)=12320[/tex]So, Total cost of producing 200 items is 12320Now Average cost per item = [tex]\frac{\text{Total cost}}{\text{No. of items}}[/tex] Average cost per item= [tex]\frac{12320}{200}[/tex]Average cost per item=61.6So,  the average cost per item when 200 items are produced is 61.6 .b) 2000 items Cost function : [tex]C(x)=7.6x + 10,800[/tex]Substitute x = 2000 [tex]C(2000)=7.6(2000)+ 10,800[/tex][tex]C(2000)=26000[/tex]So, Total cost of producing 2000 items is 26000Now Average cost per item = [tex]\frac{\text{Total cost}}{\text{No. of items}}[/tex] Average cost per item= [tex]\frac{26000}{2000}[/tex]Average cost per item=13So, the average cost per item when 2000 items are produced is 13.c) 5000 itemsCost function : [tex]C(x)=7.6x + 10,800[/tex]Substitute x = 5000 [tex]C(5000)=7.6(5000)+ 10,800[/tex][tex]C(5000)=48800[/tex]So, Total cost of producing 5000 items is 48800Now Average cost per item = [tex]\frac{\text{Total cost}}{\text{No. of items}}[/tex] Average cost per item= [tex]\frac{48800}{5000}[/tex]Average cost per item=9.76 So, the average cost per item when 5000 items are produced is 9.76