Question

5. As part of the efforts to remain competitive, Engine-X tries to keep up with the latest in production technology. The company spends a great deal of effort testing new technologies for its sports engine division where competition is high. When a new technology is first introduced, firms often experience learning, resulting in a gradual decrease in the time required to produce successive units. Generally, the rate of improvement declines until production time levels off. On typical example is the production of new turbocharger systems at Engine-X. To determine the time required to produce these systems, Engine-X produced 50 units on its production line; test results are given in the Excel file Turbo. Because Engine-X is continuously developing new technology, understanding the rate of learning can be useful in estimating future production costs without having to run expensive prototype trials.

5a. Plot the data in the Turbo file and estimate the best fit line function.

5b. Evaluate the function’s goodness of fit.

5c. Estimate the time required to produce 30 turbocharger units.

DATA:

Turbocharge Production Time
Production (units)	Production Time (min)
1	65.1
2	62.3
3	60.4
4	58.7
5	58.1
6	56.9
7	57.0
8	56.5
9	55.1
10	54.3
11	53.7
12	53.2
13	52.8
14	52.5
15	52.1
16	51.8
17	51.5
18	51.3
19	50.9
20	50.5
21	50.2
22	50.0
23	49.7
24	49.5
25	49.3
26	49.4
27	49.1
28	49.0
29	48.8
30	48.5
31	48.3
32	48.2
33	48.1
34	47.9
35	47.7
36	47.6
37	47.4
38	47.1
39	46.9
40	46.8
41	46.7
42	46.6
43	46.5
44	46.5
45	46.2
46	46.3
47	46.0
48	45.8
49	45.7
50	45.6

Answer 1

5a)

b) The estimated equation will be
Time = 58.18367Production - 0.146305*Production2.
The goodness of fit is 0.84. This implies that the independent variable production units explain
84% variation in production time.
c)
Time required to produce 30 units will be 1613.84 minutes.