The table below provides shipping rates for packages using UPS next day air or g
ID: 377228 • Letter: T
Question
The table below provides shipping rates for packages using UPS next day air or ground service options. The rates vary according to both the weight of the package and the distance of the shipment (larger numbered zones are farther away). Note that the zone number also indicates the number of days required to deliver a package using ground service. For example, it would take three days and cost $7.40 to send a 10-pound package to zone 3 using ground service.
Table of Shipping Rates
Next Day Service Weight
Domestic Zones
1
2
3
4
5
6
7
1 Lbs.
$
16.25
$
19.25
$
22.75
$
24.75
$
27.00
$
28.25
$
29.00
2
$
17.25
$
20.75
$
25.50
$
27.75
$
30.25
$
31.25
$
32.00
3
$
19.00
$
21.75
$
28.25
$
30.50
$
33.50
$
34.75
$
35.50
4
$
20.00
$
22.75
$
31.00
$
33.50
$
36.50
$
37.75
$
38.50
5
$
21.25
$
24.25
$
33.50
$
36.25
$
39.50
$
40.75
$
41.75
6
$
22.00
$
25.25
$
36.00
$
39.00
$
42.75
$
44.00
$
45.00
7
$
22.75
$
27.00
$
38.50
$
42.00
$
46.00
$
47.00
$
48.25
8
$
23.75
$
28.25
$
41.00
$
44.75
$
49.25
$
50.25
$
51.25
9
$
24.50
$
29.75
$
43.75
$
47.50
$
52.50
$
53.75
$
54.50
10
$
25.25
$
31.00
$
46.25
$
50.25
$
55.25
$
56.75
$
57.75
11
$
26.25
$
32.50
$
48.75
$
52.75
$
58.00
$
60.00
$
60.75
12
$
27.00
$
33.50
$
51.25
$
55.50
$
60.75
$
63.00
$
63.75
13
$
27.75
$
34.75
$
53.75
$
58.00
$
63.25
$
65.75
$
66.50
14
$
28.50
$
36.00
$
55.75
$
60.50
$
65.75
$
68.50
$
69.25
15
$
29.50
$
37.50
$
58.00
$
63.00
$
68.25
$
70.75
$
72.00
Ground Service Weight
Domestic Zones - Transit Time in Days
1
2
3
4
5
6
7
1 Lbs.
$
4.75
$
4.90
$
5.25
$
5.35
$
5.65
$
5.70
$
5.85
2
$
4.85
$
5.15
$
5.65
$
5.80
$
6.25
$
6.40
$
6.80
3
$
5.00
$
5.40
$
6.00
$
6.25
$
6.70
$
6.90
$
7.55
4
$
5.15
$
5.60
$
6.30
$
6.60
$
7.10
$
7.30
$
8.05
5
$
5.40
$
5.80
$
6.60
$
6.95
$
7.40
$
7.75
$
8.55
6
$
5.55
$
6.00
$
6.75
$
7.20
$
7.65
$
8.05
$
8.85
7
$
5.75
$
6.15
$
6.90
$
7.45
$
7.95
$
8.35
$
9.25
8
$
6.00
$
6.35
$
7.10
$
7.60
$
8.25
$
8.75
$
9.90
9
$
6.20
$
6.55
$
7.25
$
7.80
$
8.45
$
9.25
$
10.55
10
$
6.40
$
6.70
$
7.40
$
8.00
$
8.80
$
9.90
$
11.25
11
$
6.60
$
6.90
$
7.55
$
8.25
$
9.20
$
10.60
$
12.05
12
$
6.80
$
7.10
$
7.70
$
8.45
$
9.60
$
11.35
$
12.95
13
$
7.00
$
7.35
$
7.85
$
8.65
$
10.05
$
12.05
$
13.80
14
$
7.15
$
7.55
$
8.00
$
8.85
$
10.60
$
12.75
$
14.65
15
$
7.35
$
7.80
$
8.15
$
9.05
$
11.15
$
13.45
$
15.55
Suppose you have a package weighing 10 pounds that needs to be shipped to zone 6. The value of the material is $8,000 and the annual inventory holding rate is 30 percent of the product value.
a-1. Calculate the total shipping and transit inventory cost using the air and ground transportations. (Use 365 days in a year. Do not round intermediate calculations. Round your answers to 2 decimal places.)
a-2. Which transportation mode (air or ground) minimizes the total shipping and transit inventory cost? (Round your answer to 2 decimal places.)
b. How high would the inventory holding rate have to be in order to justify next day air service? (Use 365 days in a year. Do not round intermediate calculations. Round up your answer to the next whole number.)
Table of Shipping Rates
Next Day Service Weight
Domestic Zones
1
2
3
4
5
6
7
1 Lbs.
$
16.25
$
19.25
$
22.75
$
24.75
$
27.00
$
28.25
$
29.00
2
$
17.25
$
20.75
$
25.50
$
27.75
$
30.25
$
31.25
$
32.00
3
$
19.00
$
21.75
$
28.25
$
30.50
$
33.50
$
34.75
$
35.50
4
$
20.00
$
22.75
$
31.00
$
33.50
$
36.50
$
37.75
$
38.50
5
$
21.25
$
24.25
$
33.50
$
36.25
$
39.50
$
40.75
$
41.75
6
$
22.00
$
25.25
$
36.00
$
39.00
$
42.75
$
44.00
$
45.00
7
$
22.75
$
27.00
$
38.50
$
42.00
$
46.00
$
47.00
$
48.25
8
$
23.75
$
28.25
$
41.00
$
44.75
$
49.25
$
50.25
$
51.25
9
$
24.50
$
29.75
$
43.75
$
47.50
$
52.50
$
53.75
$
54.50
10
$
25.25
$
31.00
$
46.25
$
50.25
$
55.25
$
56.75
$
57.75
11
$
26.25
$
32.50
$
48.75
$
52.75
$
58.00
$
60.00
$
60.75
12
$
27.00
$
33.50
$
51.25
$
55.50
$
60.75
$
63.00
$
63.75
13
$
27.75
$
34.75
$
53.75
$
58.00
$
63.25
$
65.75
$
66.50
14
$
28.50
$
36.00
$
55.75
$
60.50
$
65.75
$
68.50
$
69.25
15
$
29.50
$
37.50
$
58.00
$
63.00
$
68.25
$
70.75
$
72.00
Explanation / Answer
a-1.
Air transportation cost = $ 56.75
Transit inventory cost = Inventory value * (annual inventory holding rate/365) * transit time = 8000*(30%/365)*1 = 6.575
Total shipping and transit inventory cost using air transportation = 56.75+6.575 = $ 63.33
_______
Ground transportation cost = $ 9.90
Transit inventory cost = Inventory value * (annual inventory holding rate/365) * transit time = 8000*(30%/365)*6 = 39.45
Total shipping and transit inventory cost using air transportation = 9.90+39.45 = $ 49.35
a-2.
Ground transportation minimizes the total shipping and transit inventory cost.
b. The target inventory holding rate (h) is such that total shipping and transit inventory cost of both ground and air transportation mode are equal. Therefore,
56.75 + 8000*(1/365)*h = 9.9 + 8000*(6/365)*h , solving it for h, we get
h = (56.75-9.9)/(8000*5/365) = 0.4275 or 43 % (rounded up)
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