Question

uppose that the dollar cost of producing x appliances is ​c(x)equals900plus80xminus0.2xsquared. a. Find the average cost per appliance of producing the first 150 appliances. b. Find the marginal cost when 150 appliances are produced. c. Show that the marginal cost wh

Answer 1

Answer with Step-by-step explanation:

We are given that

C(x)=
`900+80x-0.2x^2`

a.x=150

Substitute the value of x

Total cost of 150 appliances=
`900+80(150)-0.2(150)^2=`$8400

Average cost per appliance=
`(total\;cost\;of\;objects)/(number\;of\;objects)=(8400)/(150)`=$56

b.Differentiate w.r.t x

`(dC)/(dx)=80-0.4x`

Substitute x=150

Marginal cost when 150 appliances are produced

`(dC)/(dx)=80-0.4(150)=`$20

c.Cost of 151 appliances=
`900+80(151)-0.2(151)^2=`$8419.8

Cost of 151th appliance=Cost of 151 appliances-Cost of 150 appliances

Cost of 151th appliance=$8419.8-$8400=
`19.8\approx`$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 .