Answer with Step-by-step explanation:
We are given that
C(x)=[tex]900+80x-0.2x^2[/tex]
a.x=150
Substitute the value of x
Total cost of 150 appliances=[tex]900+80(150)-0.2(150)^2=[/tex]$8400
Average cost per appliance=[tex]\frac{total\;cost\;of\;objects}{number\;of\;objects}=\frac{8400}{150}[/tex]=$56
b.Differentiate w.r.t x
[tex]\frac{dC}{dx}=80-0.4x[/tex]
Substitute x=150
Marginal cost when 150 appliances are produced
[tex]\frac{dC}{dx}=80-0.4(150)=[/tex]$20
c.Cost of 151 appliances=[tex]900+80(151)-0.2(151)^2=[/tex]$8419.8
Cost of 151th appliance=Cost of 151 appliances-Cost of 150 appliances
Cost of 151th appliance=$8419.8-$8400=[tex]19.8\approx[/tex]$20
Hence, the marginal cost when 150 appliances are produced is approximately equal to the cost of producing one more appliance after the first 150 have been made .
