Problem 1 - National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows:
|
Month
|
Sales
(000)Units
|
|
Feb.
|
17
|
|
Mar.
|
17
|
|
Apr.
|
11
|
|
May.
|
25
|
|
Jun.
|
16
|
|
Jul.
|
25
|
|
Aug.
|
22
|
a. Forecast September sales volume using each of the following:
(1) A linear trend equation.
(2) A five-month moving average.
(3) Exponential smoothing with a smoothing constant equal to .30, assuming a March forecast of 16(000). (Round your intermediate forecast values and final answer to 2 decimal places)
(4) The naive approach.
(5) A weighted average using .50 for August, .20 for July, and .30 for June.
Problem 2 - Freight car loadings over an 18-week period at a busy port are as follows:
|
Week
|
Number
|
Week
|
Number
|
Week
|
Number
|
|
1
|
310
|
7
|
405
|
13
|
480
|
|
2
|
330
|
8
|
425
|
14
|
495
|
|
3
|
350
|
9
|
445
|
15
|
535
|
|
4
|
330
|
10
|
425
|
16
|
555
|
|
5
|
350
|
11
|
445
|
17
|
575
|
|
6
|
365
|
12
|
465
|
18
|
595
|
a. Determine a linear trend line for expected freight car loadings.
b. The manager intends to install new equipment when the volume exceeds 890 loadings per week. Assuming the current trend continues, in which week (at the earliest) should the loading volume reach that level?
Problem 3 - An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft = 127 + 2.1t, and it was developed using data from periods 1 through 10. Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used?
|
t
|
Units Sold
|
|
11
|
145
|
|
12
|
150
|
|
13
|
148
|
|
14
|
143
|
|
15
|
154
|
|
16
|
149
|
|
17
|
152
|
|
18
|
156
|
|
19
|
158
|
|
20
|
164
|
Problem 4 - Timely Transport provides local delivery service for a number of downtown and suburban businesses. Delivery charges are based on distance and weight involved for each delivery: 20 cents per pound and 20 cents per mile. Also, there is a $10 handling fee per parcel.
a. Develop an expression that summarizes delivery charges. (Enter your answers as dollar amounts to 2 decimal places (x1 = weight, x2 = distance). Omit the "tiny_mce_markerquot; sign in your response.)
b. Determine the delivery charge for transporting a 40-pound parcel 30 miles. (Do not round your intermediate calculation. Round your answer to 2 decimal places. Omit the "tiny_mce_markerquot; sign in your response.)
Problem 5 - The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .90, and the other has a reliability of .94.
a. What is the reliability of the computer?
b. A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability.
c. If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .98, what is the overall reliability of the system?