A golf ball manufacturer knows the cost associated with various hourly production levels, given below.Production Costs for Golf BallsProduction(hundred balls b)Cost(dollars C)24735443111497145311756520623(a) Write a cubic model for the data. (Round all numerical values to three decimal places.)C(b) = 0.0669b3 – 2.899962 + 54.953b + 146.35dollars is the production cost when the hourly production rate is b hundred golf balls 2sbs 20.(b) If 1000 balls are currently being produced each hour, calculate the marginal cost at that level of production. (Round your answer to two decimal places.)$ 17.25X per hundred ballsInterpret the result. (Round your numerical answer to two decimal places.)At an hourly production level of 1000 golf balls, production cost is increasingby $ 17.225X per hundred golf balls.

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Asked Dec 6, 2019
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A golf ball manufacturer knows the cost associated with various hourly production levels, given below.
Production Costs for Golf Balls
Production
(hundred balls b)
Cost
(dollars C)
247
354
431
11
497
14
531
17
565
20
623
(a) Write a cubic model for the data. (Round all numerical values to three decimal places.)
C(b) = 0.0669b3 – 2.899962 + 54.953b + 146.35
dollars is the production cost when the hourly production rate is b hundred golf balls 2
sbs 20.
(b) If 1000 balls are currently being produced each hour, calculate the marginal cost at that level of production. (Round your answer to two decimal places.)
$ 17.25
X per hundred balls
Interpret the result. (Round your numerical answer to two decimal places.)
At an hourly production level of 1000 golf balls, production cost is increasing
by $ 17.225
X per hundred golf balls.
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A golf ball manufacturer knows the cost associated with various hourly production levels, given below. Production Costs for Golf Balls Production (hundred balls b) Cost (dollars C) 247 354 431 11 497 14 531 17 565 20 623 (a) Write a cubic model for the data. (Round all numerical values to three decimal places.) C(b) = 0.0669b3 – 2.899962 + 54.953b + 146.35 dollars is the production cost when the hourly production rate is b hundred golf balls 2 sbs 20. (b) If 1000 balls are currently being produced each hour, calculate the marginal cost at that level of production. (Round your answer to two decimal places.) $ 17.25 X per hundred balls Interpret the result. (Round your numerical answer to two decimal places.) At an hourly production level of 1000 golf balls, production cost is increasing by $ 17.225 X per hundred golf balls.

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Expert Answer

Step 1

(a)  Use excel and compute the cubic model for the given data as follows.

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Production (hundred Cost (dollars C) ball b) 247 5 354 431 11 497 14 531 17 565 20 623 Production - Cost 700 600 500 400 300 200 100 10 15 20 25 Production aso)

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Step 2

 

Use cubic regression feature in online calculator and find the least square best fit as follows.

 

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data (12, 247), (5, 354), (8, 431), (11, 497), (14, 531), (17, 565), (20, 623)) fit polynomial of degree 3 or less model Least-squares best fit: 0.0668724 x - 2.89991 x² +54.9533 x + 146.349 Round to three decimal places as, 0.067b3-2.900b2+54.953b+146.349. Thus, required C(b) = 0.067b3 - 2.9b2 + 54.953b +146.349 the cubic model for the given data is

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Step 3

(b) Calculate the marginal cost as follows.

In order to find the marginal cost, first ...

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C(b) = ( (0.067b3 – 2.9b² +54.953b+146.349) db = 3(0.067)b? – 2(2.9)b+54.953(1)+ 0 = 0.201b? – 5.8b+ 54.953 Therefore, the marginal cost is C'(b) = 0.201b2 – 5.8b + 54.953 per hundred balls.

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