A golf ball manufacturer knows the cost associated with various hourly production levels, given below. Production Costs for Golf Balls Production Cost (hundred balls b) (dollars C) 249 357 431 500 534 562 622 (a) Write the function for the cubic model that gives the production costs for golf balls in dollars where b is the hourly production level in hundred balls, with data from 2 s b s 20. (Round all numerical values to three decimal places.) c : 147.907 + 55.20517 2.9212;2 + 0.067b3 dollars V (b) If 1000 balls are currently being produced each hour, calculate the marginal cost at that level of production. (Round your answer to three decimal places.) $ 164.792 X per hundred balls Interpret the result. (Round your numerical answer to three decimal places.) At an hourly production level of 1000 golf balls, production cost is y by $ 164.792 x per hundred golf balls. (c) Construct the function for the model that gives average cost in dollars per hundred balls where b is the hourly production level in hundred balls, with data from 2 S b s 20. (Round all numerical values to three decimal places.) E(b) = M + 55.205 2.92117 -l- 0.067172 dollars per hundred balls I) V (d) Calculate the rate of change of average cost for hourly production levels of 1000 golf balls. (Round your answer to three decimal places.) $ 3.060 v per hundred balls per hundred balls Interpret the result. (Round your numerical answer to three decimal places.) At an hourly production level of 1000 golf balls, average production cost is decreasing v| y by $ |3.060 y per hundred golf balls per hundred golf balls