For this assignment, you submit answers by question parts. The number of submiss

Question

For this assignment, you submit answers by question parts. The number of submissions remaining for each equation part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1300 + 15x - d. 1x^2 + 0.0005x^3. (a) Find the marginal cost function. c(x) = (b) Find C(400) and explain its meaning. What does it predict? CT(400) = and this is the rate at which costs are increasing with x =. C(400) respect to the production level when x = C(4000 predicts the cost of producing the yard. (c) Compare c(400) with the cost of manufacturing the 401st yard of fabric. (Round your answers to four decimal places.) The cost of manufacturing the 401st yard of fabric is C(401) - C(400) = -23, 300 =, which is approximately C(400).

Explanation / Answer

a)
C(x) = 1300 +15*x -0.1*x^2 + 0.0005*x^3

marginal cost,
C'(x) = 15 - 0.2*x + 0.0015*x^2

b)
C'(x) = 15 - 0.2*x + 0.0015*x^2
put x=400
C'(400) = 15 - 0.2*400 + 0.0015*400^2
= 175
C'(400) = 175 and this is the arte at whoich costs are increasing with respect to the production level when x=400.
C(400) predicts the cost of producing 400 yards

C)
C(x) = 1300 +15*x -0.1*x^2 + 0.0005*x^3
C(400) = 1300 +15*400 -0.1*(400)^2 + 0.0005*(400)^3
= 23300
C(401) = 1300 +15*401 -0.1*(401)^2 + 0.0005*(401)^3
= 23475.5

C(401) - C(400) = 2347.5 - 23300 = 175.5 which is approximately C'(400)

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