Section 8

file_08.xlsx

P13-10-Slow

Renting a copier							10. The Decision Sciences Department is trying to determina whether to rent a slow or fast copier.
							The department believes that an employee's time is worth $15 per hour. The slow copier rents for $4 per
Inputs (for slow system)							hour, and takes an employee an average of 10 minutes to complete copying. The fast copier rents for
Unit of time	hour						$15 per hour, and it takes an employee an average of 6 minutes to complete copying.
Arrival rate	1	customers/hour					On average, four employees per hous need to use the copying machine. (Assume the copying
Service rate	2	customers/hour					times and interarival times to the copying machine are exponetially distributed.) Which machine should
							the department rent to minimize expeted total cost per hour?
Outputs
Direct outputs from inputs			Distribution of number in system		Distribution of time in queue
Mean time between arrivals	1.000	hours	n (customers)	P(n in system)	t (in hours)	P(wait > t)
Mean time per service	0.500	hours	4	0.031	2.000	0.068
Traffic intensity	0.500
Summary measures
Expected number in system	1.000	customers
Expected number in queue	0.500	customers
Expected time in system	1.000	hours
Expected time in queue	0.500	hours
Percentage who don't wait in queue	50.0%
Cost analysis
Employee cost/hr
Rental cost/hour
Waiting cost/hour
Total Cost/hour

Problem 11.11

The fast copier is better (expected total cost of $25 versus $34 for slow copier).

Renting a copier
Inputs (for slow system)
Unit of time	hour
Arrival rate	1	customers/hour
Service rate	2	customers/hour
Outputs
Direct outputs from inputs			Distribution of number in system		Distribution of time in queue
Mean time between arrivals	1.000	hours	n (customers)	P(n in system)	t (in hours)	P(wait > t)
Mean time per service	0.500	hours	4	0.031	2.000	0.068
Traffic intensity	0.500
Summary measures
Expected number in system	1.000	customers
Expected number in queue	0.500	customers
Expected time in system	1.000	hours
Expected time in queue	0.500	hours
Percentage who don't wait in queue	50.0%
Cost analysis
Employee cost/hr
Rental cost/hour
Waiting cost/hour
Total Cost/hour

Problem 11.11

Day	Peak Load Christopher J. Zappe, Ph.D.: In megawatts.	Daily High Temperature Christopher J. Zappe, Ph.D.: In degrees F.	32. A power company located in southern Alabama wants to predict the peak power load (i.e., the maximum
1	118.5	89	amount of power that must be generated each day to meet demand) as a function of the daily high temperature
2	136.0	94	(X.) A random sample of 25 summer days is chosen, and the peak power load and the high temperature are
3	143.6	100	recorded each day. The file P14_32.xlsx contains these observations
4	153.2	97
5	140.7	95	a. Create a scatter plot for these data. Comment on the observed relationship between Y and X.
6	151.9	100
7	135.1	92	b. Estimate an appropriate regression equation to predict the peak power load for this power company.
8	178.2	106	Interpret the estimated regression coefficients.
9	101.6	67
10	96.5	67	c. Analyze the estimated equation's residuals. Do they suggest that the regression equation is adequate? If not,
11	103.9	74	return to part B and revise your equation. Continue to revise the equation until the results are satisfactory.
12	113.4	84
13	106.2	79	d. use your final equation to predict the peak power load on a summer day with a high temperature of 100 degrees.
14	111.4	85
15	116.5	89
16	96.3	68
17	150.1	98
18	105.1	86
19	114.7	87
20	189.3	108
21	131.7	96
22	100.9	76
23	92.5	71
24	132.0	90
25	116.4	88

Day	Peak Load Christopher J. Zappe, Ph.D.: In megawatts.	Daily High Temperature Christopher J. Zappe, Ph.D.: In degrees F.
1	118.5	89
2	136.0	94
3	143.6	100
4	153.2	97
5	140.7	95
6	151.9	100
7	135.1	92
8	178.2	106
9	101.6	67
10	96.5	67
11	103.9	74
12	113.4	84
13	106.2	79
14	111.4	85
15	116.5	89
16	96.3	68
17	150.1	98
18	105.1	86
19	114.7	87
20	189.3	108
21	131.7	96
22	100.9	76
23	92.5	71
24	132.0	90
25	116.4	88

Month	Advertising	Units Sold	35. The file P14_35.xlsx contains the amount of money spent advertising a product (in thousands of dollars)
1	$1,000	4,000,000	and the number of units sold (in millions) for eight months.
2	$2,000	4,800,000
3	$3,000	5,000,000	a. Assume that the only factor influencing monthly sales is advertising. Fit the following two curves to these
4	$20,000	7,500,000	data: linear (Y = a+bX) and power (Y=aXb). Which equation best fits the data?
5	$30,000	8,000,000
6	$50,000	9,000,000	b. Interpret the best fitting equation.
7	$80,000	9,900,000
8	$100,000	10,200,000	c. Using the best fitting equation, predict sales during a month in which $60,000 is spent on advertising.