Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.006
ID: 2882303 • Letter: S
Question
Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.006x^3 + 0.07x^2 + 14x + 600, and currently 90 chairs are produced monthly. What is the current monthly cost? What would be the additional cost of increasing production to 93 chairs monthly? What is the marginal cost when x = 90? Use the marginal cost to estimate the difference in cost between producing 90 and 92 chairs per month. Use the answer from part (d) to predict C(92). The current monthly cost is (Round to the nearest cent as needed.) The additional cost of increasing production to 93 chairs monthly is (Round to the nearest cent as needed.) The marginal cost when x = 90 is (Round to the nearest cent as needed.) Using the marginal cost found in part c), the difference between producing 90 and 92 chairs per month is (Round to the nearest cent as needed.) C(92) = (Round to the nearest cent as needed.)Explanation / Answer
C = 0.006x^3 + 0.07x^2 + 14x + 600
a) Plug in x = 90 :
C(90 chairs) = 0.006(90)^3 + 0.07(90)^2 + 14(90) + 600
6801 dollars ----> ANSWER
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b) Plug in x = 93 :
0.006(93)^3 + 0.07(93)^2 + 14(93) + 600
= 7333.57 dollars
Additional cost = 7333.57 - 6801
532.57 dollars ---> ANSWER
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c) Marginal cost :
C' = 0.018x^2 + 0.14x + 14
Plug in x = 90 :
0.018(90)^2+ 0.14(90) + 14
172.4 dollars per chair ----> ANSWER
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d)
C'(90) = 172.4 dollars per chair
C(92) = C(90) + C'(90) * (92 - 90)
C(92) - C(90) = 172.4 * 2
344.8 dollars -----> ANSWER
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e)
C(92) :
C(92) = C(90) + 344.8
C(92) = 6801 + 344.8
7145.8 dollars -----> ANSWER
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