Suppose that the dollar cost of producing x appliances is c(x) = 1200+ 70x ? 0.2

Question

Suppose that the dollar cost of producing x appliances is c(x) = 1200+ 70x ? 0.2x^2. a. Find the average cost per appliance of producing the first 120 appliances. b. Find the marginal cost when 120 appliances are produced. c. Show that the marginal cost when 120 appliances are produced is approximately the cost of producing one more appliance after the first 120 have been made, by calculating the latter cost directly. The average cost per appliance of producing the first 120 appliances is $ 69.00 / appliance. (Round to the nearest cent as needed.)

Explanation / Answer

c(x) = 1200 + 70x - 0.2x^2

c(120) = 1200 + 70(120) - 0.2(120)^2

c(120) = 6720 ---> this is the total cost of producing 120 appliances

So, average cost per appliance = 6720 / 120 = 56

So, average cost = 56 dollars ------> FIRST ANSWER

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b) Marginal cost : To find marginal cost, we have to derive the cost equation

c(x) = 1200 + 70x - 0.2x^2

Deriving :

c'(x) = 70 - 0.4x

Plug in 120 :

c'(120) = 70 - 0.4(120)

c'(120) = 22 ---> SECOND ANSWER

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c) c(120) = 6720

Now, c(121) = 1200 + 70(121) - 0.2(121)^2 = 6741.8

Now, as can be seen, cost of the 121st appliance = c(121) - c(120) = 6741.8 - 6720 = 21.8, which is almost equal to 22, which was our answer in part B

Hence proved!

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