Cost Analysis 2: Piston Corporation's products are replacement automobile parts. Piston had experienced a rather stable growth in sales in recent years and had been required to increase its capacity regularly. The executive officers had been asked by Piston's directors to formulate a proposal for expansion and price adjustments. Quarterly data were obtained on manufacturing costs per unit (in hundreds of dollars), production level (a proportion of the total capacity), and the index of direct material and direct labor costs for a five-year period (These data are in the worksheet entitled "PISTON5").
Begin by fitting the linear model to predict the average cost per unit (COST) from production level (x1 = PROD) and the index of direct material and direct labor costs (x2 = INDEX).
COST PROD INDEX
3.65 0.85 80
4.22 0.78 93
4.29 0.82 107
5.43 0.64 115
6.42 0.5 130
5.71 0.62 128
5.39 0.7 116
3.99 0.9 92
4.08 0.94 94
4.38 1 110
4.28 1.04 115
4.42 0.82 117
5.11 0.75 128
4.88 0.84 134
4.99 0.86 135
4.57 0.9 135
4.84 0.94 139
5.16 0.8 142
5.67 0.72 147
6.26 0.6 150
Regardless of your decision above, use the Reciprocal Model to answer ALL of the questions below. Also, be sure to compute these values based on the UNROUNDED values in EXCEL. e) Predict the cost per unit for a quarter with a production level of 95% and an index of 85. (Enter your answers to two decimal places.) f) At what rate is the cost per unit changing with respect to production level for a quarter with a production level of 95% and an index of 85? (Enter your answer to two decimal places.) At what rate is the cost per unit changing with respect to index for a quarter with a production level of 95% and an index of 857 (Enter your answer to two decimal places.) 9) Predict the cost per unit for a quarter with a production level of 70% and an index of 150. (Enter your answers to two decimal places.) h) At what rate is the cost per unit changing with respect to production level for a quarter with a production level of 70% and an index of 150? (Enter your answer to two decimal places.)