Suppose that the dollar cost ,C, of producing x washing machines is given by: C(

Question

Suppose that the dollar cost ,C, of producing x washing machines is given by:

C(x)=2700 +130x -.09x^2.

A. Find the average cost per machine of producing the first 200 washing machines.

B. Find the marginal cost of , when 200 washing machines are produced and then again when 400 washing machines are produced.

C.Is it cheaper to produce the 201st washing machine or the 401st machine?

D. Calculate the acutal cost of producing the 201st and 401st Machine.

E. compare your answer in b and d. were they they close? why are they not the same ?

Explanation / Answer

A) average cost means C(x)/x

C(200)/200 = 25100/200 = 125.50

B) marginal cost = C ' (x) = 130 - .18x

C ' (200) = 94

C ' (400) = 58

C) Marginal cost is the cost of producing an additional unit past the specfied x value.

C ' (200) = 94 means the 201st washing machine costs an additional $94

C ' (400) = 58 means the 401st washing machine costs an additional $58

The 401st machine is cheaper.

D) actual cost is a difference based on C(x)

201st machine: C(201) - C(200) = 25193.91 - 25100 = $93.91

401st machine: C(401) - C(400) = 40357.91 - 40300 = $57.91

E) B and D values are close but not exactly the same because the derivative assumes cost increases by the same amount as exactly at the indicated x value, even though the slopes all along the C(x) curve are different.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.